Home
Curriculum Vitae
Publications
Teaching
Research
Editorial Activities
Supervision
Imprint
Last modification:
September 24, 2024
 
Patrick Winkert
patrick_winkert Technische Universität Berlin
Institut für Mathematik
Sekretariat MA 1-0
MA 669
Straße des 17. Juni 136
10623 Berlin, Germany
+49 - 30 - 314 - 2 74 87
winkert(at)math.tu-berlin.de
Website at TU Berlin
Google Scholar
ORCID
Patrick Winkert
Curriculum Vitae
Education
  • 2015: Habilitation in Mathematics (postdoctoral qualification, Dr.rer.nat.habil.), Thesis: Global a priori bounds and multiplicity results for quasilinear elliptic equations and inequalities, Technische Universität Berlin, Berlin, Germany
  • 2009: Ph.D. in Mathematics (Dr.rer.nat.), Thesis: Comparison principles and multiple solutions for nonlinear elliptic problems, Martin-Luther-Universität Halle-Wittenberg, Halle, Germany,
  • 2006: Master in Mathematics (Diploma in Mathematics), Thesis: T-symmetrische Tensor-Differentialformen mit logarithmischen Polen, Martin-Luther-Universität Halle-Wittenberg, Halle, Germany
Employment
  • since 2019: Research Assistant (permanent), Technische Universität Berlin, Berlin, Germany
  • since 2016: Privatdozent, Technische Universität Berlin, Berlin, Germany
  • Fall 2017: Substitute Professor 'Analysis', Martin-Luther-Universität Halle-Wittenberg, Halle, Germany
  • Spring 2017: Guest Professor 'Applied Analysis', Humboldt-Universität zu Berlin, Berlin, Germany
  • Fall 2016: Substitute Professor 'Analysis', Martin-Luther-Universität Halle-Wittenberg, Halle, Germany
  • Spring 2016: Substitute Professor 'Applied Analysis', Martin-Luther-Universität Halle-Wittenberg, Halle, Germany
  • 2009 – 2019: Research Assistant, Technische Universität Berlin, Berlin, Germany
  • 2006 – 2009: Research Assistant, Martin-Luther-Universität Halle-Wittenberg, Halle, Germany
Patrick Winkert
Publications
Monographs
  1. N.S. Papageorgiou, P. Winkert, Applied Nonlinear Functional Analysis. An Introduction, Second Revised Edition, De Gruyter, Berlin, 2024, xii+722 pp. De Gruyter
  2. N.S. Papageorgiou, P. Winkert, Applied Nonlinear Functional Analysis. An Introduction, De Gruyter, Berlin, 2018, x+612 pp.
    De Gruyter
Editorials
  1. P. Candito, R. Livrea, P. Winkert, Special issue on the occasion of the 70th birthday of Professor Siegfried Carl, Nonlinear Anal. Real World Appl. 74 (2023), Paper No. 103959. Preprint   Journal   
Refereed Articles
  1. G.M. Figueiredo, M.T.O. Pimenta, P. Winkert, The asymptotic behavior of constant sign and nodal solutions of (p,q)-Laplacian problems as p goes to 1, Nonlinear Anal. 251 (2025), Paper No. 113677, 14 pp. Preprint   Journal   
  2. Á. Crespo-Blanco, L. Gasiński, P. Winkert, Least energy sign-changing solution for degenerate Kirchhoff double phase problems, J. Differential Equations 411 (2024), 51–89. Preprint   Journal   arXiv
  3. F. Vetro, P. Winkert, Logarithmic double phase problems with convection: existence and uniqueness results, Commun. Pure Appl. Anal. 23 (2024), no. 9, 1325–1339. Preprint   Journal   
  4. X. He, Y. Meng, P. Winkert, Multiple bound states for a class of fractional critical Schrödinger-Poisson systems with critical frequency, J. Math. Phys. 65 (2024), no. 7, Paper No. 071502, 23 pp. Preprint   Journal   
  5. S. Carl, P. Winkert, Parabolic double phase obstacle problems, Nonlinear Anal. Real World Appl. 80 (2024), Paper No. 104169, 14 pp. Preprint   Journal   
  6. W. Liu, G. Dai, P. Winkert, S. Zeng, Multiple positive solutions for quasilinear elliptic problems in expanding domains, Appl. Math. Optim. 90 (2024), no. 1, Paper No. 13, 23 pp. Preprint   Journal   
  7. M.M. Frisch, P. Winkert, Boundedness, existence and uniqueness results for coupled gradient dependent elliptic systems with nonlinear boundary condition, Adv. Nonlinear Anal. 13 (2024), no. 1, Paper No. 20240009, 22 pp. Preprint   Journal   
  8. F. Borer, S. Carl, P. Winkert, Elliptic p-Laplacian systems with nonlinear boundary condition, J. Math. Anal. Appl. 538 (2024), no. 2, Paper No. 128421. Preprint   Journal   arXiv
  9. E. Amoroso, G. Bonanno, G. D'Aguì, P. Winkert, Two solutions for Dirichlet double phase problems with variable exponents, Adv. Nonlinear Stud. 24 (2024), no. 3, 734–747. Preprint   Journal   
  10. H. Tao, L. Li, P. Winkert, Existence and multiplicity of solutions for fractional Schrödinger-p-Kirchhoff equations in RN, Forum Math., accepted 2024. Preprint   Journal   
  11. N.S. Papageorgiou, F. Vetro, P. Winkert, Sequences of nodal solutions for critical double phase problems with variable exponents, Z. Angew. Math. Phys. 75 (2024), no. 3, Paper No. 95. Preprint   Journal   
  12. W. Liu, G. Dai, P. Winkert, Multiple sign-changing solutions for superlinear (p,q)-equations in symmetrical expanding domains, Bull. Sci. Math. 191 (2024), Paper No. 103393, 21 pp. Preprint   Journal   
  13. E. Amoroso, A. Sciammetta, P. Winkert, Anisotropic (p⃗,q⃗)-Laplacian problems with superlinear nonlinearities, Commun. Anal. Mech. 16 (2024), no. 1, 1–23. Preprint   Journal   
  14. S. Zeng, V.D. Rădulescu, P. Winkert, Nonlocal double phase implicit obstacle problems with multivalued boundary conditions, SIAM J. Math. Anal. 56 (2024), no. 1, 877–912. Preprint   Journal   
  15. Á. Crespo-Blanco, P. Winkert, Nehari manifold approach for superlinear double phase problems with variable exponents, Ann. Mat. Pura Appl. (4) 203 (2024), no. 2, 605–634. Preprint   Journal   arXiv
  16. S. El Manouni, K. Perera, P. Winkert, (p,q)-Laplacian problems with parameters in bounded and unbounded domains, Houston J. Math. 49 (2023), no. 4, 921–937. Preprint   Journal   
  17. N.S. Papageorgiou, F. Vetro, P. Winkert, Sign changing solutions for critical double phase problems with variable exponent, Z. Anal. Anwend. 42 (2023), no. 1-2, 235–251. Preprint   Journal   
  18. K. Ho, P. Winkert, New embedding results for double phase problems with variable exponents and a priori bounds for corresponding generalized double phase problems, Calc. Var. Partial Differential Equations 62 (2023), no. 8, Paper No. 227, 38 pp. Preprint   Journal   arXiv
  19. K. Ho, P. Winkert, Infinitely many solutions to Kirchhoff double phase problems with variable exponents, Appl. Math. Lett. 145 (2023), Paper No. 108783, 8 pp. Preprint   Journal   arXiv
  20. H. Tao, L. Li, P. Winkert, Existence and concentration of solutions for a 1-biharmonic Choquard equation with steep potential well in RN, J. Geom. Anal. 33 (2023), no. 9, Paper No. 276, 27 pp. Preprint   Journal   
  21. F. Vetro, P. Winkert, Nodal solutions for critical Robin double phase problems with variable exponent, Discrete Contin. Dyn. Syst. Ser. S 16 (2023), no. 11, 3333–3349. Preprint   Journal   
  22. R. Arora, A. Fiscella, T. Mukherjee, P. Winkert, Existence of ground state solutions for a Choquard double phase problem, Nonlinear Anal. Real World Appl. 73 (2023), Paper No. 103914, 22 pp. Preprint   Journal   arXiv
  23. Y. Yang, W. Liu, P. Winkert, X. Yan, Existence of solutions for resonant double phase problems with mixed boundary value conditions, Partial Differ. Equ. Appl. 4 (2023), no. 3, Paper No. 18, 17 pp. Preprint   Journal   
  24. S. Zeng, Y. Bai, V.D. Rădulescu, P. Winkert, An inverse problem for a double phase implicit obstacle problem with multivalued terms, ESAIM Control Optim. Calc. Var. 29 (2023), Paper No. 30, 23 pp. Preprint   Journal   
  25. U. Guarnotta, R. Livrea, P. Winkert, The sub-supersolution method for variable exponent double phase systems with nonlinear boundary conditions, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 34 (2023), no. 3, 617–639. Preprint   Journal   arXiv
  26. R. Arora, A. Fiscella, T. Mukherjee, P. Winkert, On double phase Kirchhoff problems with singular nonlinearity, Adv. Nonlinear Anal. 12 (2023), no. 1, Paper No. 20220312, 24 pp. Preprint   Journal   arXiv
  27. Y. Liu, V.T. Nguyen, P. Winkert, S. Zeng, Coupled double phase obstacle systems involving nonlocal functions and multivalued convection terms, Monatsh. Math. 202 (2023), no. 2, 363–376. Preprint   Journal   
  28. A. Sciammetta, E. Tornatore, P. Winkert, Bounded weak solutions to superlinear Dirichlet double phase problems, Anal. Math. Phys. 13 (2023), no. 2, Paper No. 23, 18 pp. Preprint   Journal   
  29. S. Zeng, N.S. Papageorgiou, P. Winkert, Inverse problems for double-phase obstacle problems with variable exponents, J. Optim. Theory Appl. 196 (2023), no. 2, 666–699. Preprint   Journal   
  30. S. Zeng, L. Gasiński, V.D. Rădulescu, P. Winkert, Anisotropic and isotropic implicit obstacle problems with nonlocal terms and multivalued boundary conditions, Commun. Nonlinear Sci. Numer. Simul. 118 (2023), Paper No. 106997, 34 pp. Preprint   Journal   
  31. Á. Crespo-Blanco, N.S. Papageorgiou, P. Winkert, (p,q)-Equations with negative concave terms, J. Geom. Anal. 33 (2023), no. 1, Paper No. 5, 26 pp. Preprint   Journal   
  32. F. Vetro, P. Winkert, Constant sign solutions for double phase problems with variable exponents, Appl. Math. Lett. 135 (2023), Paper No. 108404, 7 pp. Preprint   Journal   
  33. G. D'Aguì, A. Sciammetta, P. Winkert, On the Fučík spectrum of the p-Laplacian with no-flux boundary condition, Nonlinear Anal. Real World Appl. 69 (2023) 103736, 17 pp. Preprint   Journal   
  34. G. D'Aguì, A. Sciammetta, E. Tornatore, P. Winkert, Parametric Robin double phase problems with critical growth on the boundary, Discrete Contin. Dyn. Syst. Ser. S 16 (2023), no. 6, 1286–1299. Preprint   Journal   
  35. S. Zeng, V.D. Rădulescu, P. Winkert, Double phase obstacle problems with multivalued convection and mixed boundary value conditions, Discrete Contin. Dyn. Syst. Ser. B 28 (2023), no. 2, 999–1023. Preprint   Journal   arXiv
  36. S. Zeng, Y. Bai, P. Winkert, J.-C. Yao, Identification of discontinuous parameters in double phase obstacle problems, Adv. Nonlinear Anal. 12 (2023), no. 1, 1–22. Preprint   Journal   
  37. C. Farkas, A. Fiscella, P. Winkert, On a class of critical double phase problems, J. Math. Anal. Appl. 515 (2022), no. 2, 126420, 16 pp. Preprint   Journal   arXiv
  38. F. Vetro, P. Winkert, Existence, uniqueness and asymptotic behavior of parametric anisotropic (p,q)-equations with convection, Appl. Math. Optim. 86 (2022), no. 2, Paper No. 18, 18 pp. Preprint   Journal   
  39. R. Arora, A. Fiscella, T. Mukherjee, P. Winkert, On critical double phase Kirchhoff problems with singular nonlinearity, Rend. Circ. Mat. Palermo (2) 71 (2022), no. 3, 1079–1106. Preprint   Journal   
  40. S. Zeng, V.D. Rădulescu, P. Winkert, Double phase obstacle problems with variable exponent, Adv. Differential Equations 27 (2022), no. 9-10, 611–645. Preprint   Journal   
  41. W. Liu, G. Dai, N.S. Papageorgiou, P. Winkert, Existence of solutions for singular double phase problems via the Nehari manifold method, Anal. Math. Phys. 12 (2022), no. 3, Paper No. 75, 25 pp. Preprint   Journal   arXiv
  42. Á. Crespo-Blanco, L. Gasiński, P. Harjulehto, P. Winkert, A new class of double phase variable exponent problems: Existence and uniqueness, J. Differential Equations 323 (2022), 182–228. Preprint   Journal   arXiv
  43. K. Ho, Y.-H. Kim, P. Winkert, C. Zhang, The boundedness and Hölder continuity of solutions to elliptic equations involving variable exponents and critical growth, J. Differential Equations 313 (2022), 503–532. Preprint   Journal   arXiv
  44. S. Zeng, V.D. Rădulescu, P. Winkert, Double phase implicit obstacle problems with convection and multivalued mixed boundary value conditions, SIAM J. Math. Anal. 54 (2022), no. 2, 1898–1926. Preprint   Journal   arXiv
  45. W. Liu, P. Winkert, Combined effects of singular and superlinear nonlinearities in singular double phase problems in RN, J. Math. Anal. Appl. 507 (2022), no. 2, 125762, 19 pp. Preprint   Journal   arXiv
  46. Á. Crespo-Blanco, N.S. Papageorgiou, P. Winkert, Parametric superlinear double phase problems with singular term and critical growth on the boundary, Math. Methods Appl. Sci. 45 (2022), no. 4, 2276–2298. Preprint   Journal   arXiv
  47. N.S. Papageorgiou, P. Winkert, A multiplicity theorem for anisotropic Robin equations, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 33 (2022), no. 1, 1–22. Preprint   Journal   arXiv
  48. S. El Manouni, G. Marino, P. Winkert, Existence results for double phase problems depending on Robin and Steklov eigenvalues for the p-Laplacian, Adv. Nonlinear Anal. 11 (2022), no. 1, 304–320. Preprint   Journal   arXiv
  49. N.S. Papageorgiou, P. Winkert, On a class of singular anisotropic (p,q)-equations, Rev. Mat. Complut. 35 (2022), no. 2, 545–571. Preprint   Journal   arXiv
  50. C. Farkas, A. Fiscella, P. Winkert, Singular Finsler double phase problems with nonlinear boundary condition, Adv. Nonlinear Stud. 21 (2021), no. 4, 809–825. Preprint   Journal   arXiv
  51. N.S. Papageorgiou, P. Winkert, Existence and nonexistence of positive solutions for singular (p,q)-equations with superdiffusive perturbation, Results Math. 76 (2021), no. 4, Paper No. 169, 20 pp. Preprint   Journal   arXiv
  52. N.S. Papageorgiou, P. Winkert, Positive solutions for singular anisotropic (p,q)-equations, J. Geom. Anal. 31 (2021), no. 12, 11849–11877. Preprint   Journal   arXiv
  53. C. Farkas, P. Winkert, An existence result for singular Finsler double phase problems, J. Differential Equations 286 (2021), 455–473. Preprint   Journal   arXiv
  54. L. Gasiński, P. Winkert, Sign changing solution for a double phase problem with nonlinear boundary condition via the Nehari manifold, J. Differential Equations 274 (2021), 1037–1066. Preprint   Journal   arXiv
  55. N.S. Papageorgiou, P. Winkert, Singular Dirichlet (p,q)-equations, Mediterr. J. Math. 18 (2021), no. 4, Paper No. 141, 20 pp. Preprint   Journal   arXiv
  56. S. Zeng, Y. Bai, L. Gasiński, P. Winkert, Convergence analysis for double phase obstacle problems with multivalued convection term, Adv. Nonlinear Anal. 10 (2021), no. 1, 659–672. Preprint   Journal   
  57. A. Bahrouni, V.D. Rădulescu, P. Winkert, Small perturbations of Robin problems driven by the p-Laplacian plus a positive potential, Topol. Methods Nonlinear Anal. 57 (2021), no. 2, 663–673. Preprint   Journal   
  58. N.S. Papageorgiou, P. Winkert, (p,q)-Equations with singular and concave convex nonlinearities, Appl. Math. Optim. 84 (2021), no. 3, 2601–2628. Preprint   Journal   arXiv
  59. S. Zeng, L. Gasiński, P. Winkert, Y. Bai, Existence of solutions for double phase obstacle problems with multivalued convection term, J. Math. Anal. Appl. 501 (2021), no. 1, 123997, 12 pp. Preprint   Journal   
  60. N.S. Papageorgiou, P. Winkert, Positive solutions for weighted singular p-Laplace equations via Nehari manifolds, Appl. Anal. 100 (2021), no. 11, 2436–2448. Preprint   Journal   arXiv
  61. A. Bahrouni, V.D. Rădulescu, P. Winkert, Double phase problems with variable growth and convection for the Baouendi-Grushin operator, Z. Angew. Math. Phys. 71 (2020), no. 6, 183. Preprint   Journal   
  62. A. Bahrouni, V.D. Rădulescu, P. Winkert, Robin fractional problems with symmetric variable growth, J. Math. Phys. 61 (2020), no. 10, 101503, 14 pp. Preprint   Journal   arXiv
  63. S. Zeng, Y. Bai, L. Gasiński, P. Winkert, Existence results for double phase implicit obstacle problems involving multivalued operators, Calc. Var. Partial Differential Equations 59 (2020), no. 5, Paper No. 176, 18 pp. Preprint   Journal   
  64. G. Marino, P. Winkert, Existence and uniqueness of elliptic systems with double phase operators and convection terms, J. Math. Anal. Appl. 492 (2020), no. 1, 124423, 13 pp. Preprint   Journal   arXiv
  65. A. Bahrouni, V.D. Rădulescu, P. Winkert, A critical point theorem for perturbed functionals and low perturbations of differential and nonlocal systems, Adv. Nonlinear Stud. 20 (2020), no. 3, 663–674. Preprint   Journal   
  66. G. Marino, P. Winkert, L∞-bounds for general singular elliptic equations with convection term, Appl. Math. Lett. 107 (2020), 106410, 6 pp. Preprint   Journal   arXiv
  67. L. Gasiński, P. Winkert, Constant sign solutions for double phase problems with superlinear nonlinearity, Nonlinear Anal. 195 (2020), 111739, 9 pp. Preprint   Journal   arXiv
  68. Y. Bai, L. Gasiński, P. Winkert, S. Zeng, W1,p versus C1: The nonsmooth case involving critical growth, Bull. Math. Sci. 10 (2020), no. 3, 2050009, 15 pp. Preprint   Journal   
  69. L. Gasiński, P. Winkert, Existence and uniqueness results for double phase problems with convection term, J. Differential Equations 268 (2020), no. 8, 4183–4193. Preprint   Journal   arXiv
  70. G. Marino, P. Winkert, Global a priori bounds for weak solutions of quasilinear elliptic systems with nonlinear boundary condition, J. Math. Anal. Appl. 482 (2020), no. 2, 123555, 19 pp. Preprint   Journal   arXiv
  71. S.A. Marano, P. Winkert, Corrigendum to ''On a quasilinear elliptic problem with convection term and nonlinear boundary condition'' [Nonlinear Anal. 187 (2019), 159–169], Nonlinear Anal. 189 (2019), 111578. Preprint   Journal   
  72. G. D'Aguì, B. Di Bella, P. Winkert, Two positive solutions for nonlinear fourth-order elastic beam equations, Electron. J. Qual. Theory Differ. Equ. 2019, Paper No. 37, 12 pp. Preprint   Journal   
  73. G. Bonanno, G. D'Aguì, P. Winkert, A two critical points theorem for non-differentiable functions and applications to highly discontinuous PDE's, Pure Appl. Funct. Anal. 4 (2019), no. 4, 709–725. Preprint   Journal   
  74. S.A. Marano, P. Winkert, On a quasilinear elliptic problem with convection term and nonlinear boundary condition, Nonlinear Anal. 187 (2019), 159–169. Preprint   Journal   
  75. D. Motreanu, P. Winkert, Existence and asymptotic properties for quasilinear elliptic equations with gradient dependence, Appl. Math. Lett. 95 (2019), 78–84. Preprint   Journal   
  76. N.S. Papageorgiou, P. Winkert, Nonlinear systems with Hartman-type perturbations, Monatsh. Math. 190 (2019), no. 2, 389–404. Preprint   Journal   
  77. G. Marino, P. Winkert, Moser iteration applied to elliptic equations with critical growth on the boundary, Nonlinear Anal. 180 (2019), 154–169. Preprint   Journal   arXiv
  78. N.S. Papageorgiou, P. Winkert, Solutions with sign information for nonlinear nonhomogeneous problems, Math. Nachr. 292 (2019), no. 4, 871–891. Preprint   Journal   
  79. N.S. Papageorgiou, P. Winkert, Singular p-Laplacian equations with superlinear perturbation, J. Differential Equations 266 (2019), no. 2-3, 1462–1487. Preprint   Journal   
  80. N.S. Papageorgiou, P. Winkert, Double resonance for Robin problems with indefinite and unbounded potential, Discrete Contin. Dyn. Syst. Ser. S 11, (2018), no. 2, 323–344. Preprint   Journal   
  81. N.S. Papageorgiou, P. Winkert, Asymmetric (p,2)-equations, superlinear at +∞, resonant at -∞, Bull. Sci. Math. 141 (2017), no. 5, 443–488. Preprint   Journal   
  82. S. El Manouni, H. Hajaiej, P. Winkert, Bounded solutions to nonlinear problems in RN involving the fractional Laplacian depending on parameters, Minimax Theory Appl. 2 (2017), no. 2, 265–283. Preprint   Journal   arXiv
  83. N.S. Papageorgiou, P. Winkert, Positive solutions for nonlinear nonhomogeneous Dirichlet problems with concave-convex nonlinearities, Positivity 20 (2016), no. 4, 945–979. Preprint   Journal   
  84. P. Winkert, R. Zacher, Global a priori bounds for weak solutions to quasilinear parabolic equations with nonstandard growth, Nonlinear Anal. 145 (2016), 1–23. Preprint   Journal   arXiv
  85. N.S. Papageorgiou, P. Winkert, Nonlinear Robin problems with a reaction of arbitrary growth, Ann. Mat. Pura Appl. (4) 195 (2016), no. 4, 1207–1235. Preprint   Journal   
  86. G. Bonanno, G. D'Aguì, P. Winkert, Sturm-Liouville equations involving discontinuous nonlinearities, Minimax Theory Appl. 1 (2016), no. 1, 125–143. Preprint   Journal   
  87. N.S. Papageorgiou, P. Winkert, Nonlinear nonhomogeneous Dirichlet equations with a superlinear nonlinearity, Results Math. 70 (2016), no. 1, 31–79. Preprint   Journal   arXiv
  88. P. Winkert, R. Zacher, Corrigendum to ''A priori bounds for weak solutions to elliptic equations with nonstandard growth'' [Discrete Contin. Dyn. Syst. Ser. S 5 (2012), 865–878], Discrete Contin. Dyn. Syst. Ser. S, published on-line as note, 2015, 1–3. Preprint   Journal   arXiv
  89. S. El Manouni, N.S. Papageorgiou, P. Winkert, Parametric nonlinear nonhomogeneous Neumann equations involving a nonhomogeneous differential operator, Monatsh. Math. 177 (2015), no. 2, 203–233. Preprint   Journal   
  90. N.S. Papageorgiou, P. Winkert, Resonant (p,2)-equations with concave terms, Appl. Anal. 94 (2015), no. 2, 342–360. Preprint   Journal   
  91. P. Winkert, On the boundedness of solutions to elliptic variational inequalities, Set-Valued Var. Anal. 22 (2014), no. 4, 763–781. Preprint   Journal   
  92. G. Bonanno, P. Winkert, Multiplicity results to a class of variational-hemivariational inequalities, Topol. Methods Nonlinear Anal. 43 (2014), no. 2, 493–516. Preprint   Journal   
  93. N.S. Papageorgiou, P. Winkert, On a parametric nonlinear Dirichlet problem with subdiffusive and equidiffusive reaction, Adv. Nonlinear Stud. 14 (2014), no. 3, 747–773. Preprint   Journal   
  94. G. Bonanno, D. Motreanu, P. Winkert, Boundary value problems with nonsmooth potential, constraints and parameters, Dynam. Systems Appl. 22 (2013), no. 2-3, 385–396. Preprint   Journal   
  95. P. Winkert, Multiplicity results for a class of elliptic problems with nonlinear boundary condition, Commun. Pure Appl. Anal. 12 (2013), no. 2, 785–802. Preprint   Journal   
  96. P. Winkert, R. Zacher, A priori bounds for weak solutions to elliptic equations with nonstandard growth, Discrete Contin. Dyn. Syst. Ser. S 5 (2012), no. 4, 865–878. Preprint   Journal   arXiv
  97. D. Motreanu, P. Winkert, On the Fučík spectrum for the p-Laplacian with Robin boundary condition, Nonlinear Anal. 74 (2011), no. 14, 4671–4681. Preprint   Journal   
  98. G. Bonanno, D. Motreanu, P. Winkert, Variational-hemivariational inequalities with small perturbations of nonhomogeneous Neumann boundary conditions, J. Math. Anal. Appl. 381 (2011), no. 2, 627–637. Preprint   Journal   
  99. P. Winkert, Multiple solution results for elliptic Neumann problems involving set-valued nonlinearities, J. Math. Anal. Appl. 377 (2011), no. 1, 121–134. Preprint   Journal   
  100. D. Motreanu, P. Winkert, Variational-hemivariational inequalities with nonhomogeneous Neumann boundary condition, Matematiche (Catania) 65 (2010), no. 2, 109–119. Preprint   Journal   
  101. P. Winkert, Sign-changing and extremal constant-sign solutions of nonlinear elliptic Neumann boundary value problems, Bound. Value Probl. 2010, Art. ID 139126, 22 pp. Preprint   Journal   
  102. P. Winkert, Local C1-minimizers versus local W1,p-minimizers of nonsmooth functionals, Nonlinear Anal. 72 (2010), no. 11, 4298–4303. Preprint   Journal   
  103. P. Winkert, L∞-estimates for nonlinear elliptic Neumann boundary value problems, NoDEA Nonlinear Differential Equations Appl. 17 (2010), no. 3, 289–302. Preprint   Journal   
  104. P. Winkert, Constant-sign and sign-changing solutions for nonlinear elliptic equations with Neumann boundary values, Adv. Differential Equations 15 (2010), no. 5-6, 561–599. Preprint   Journal   
  105. P. Winkert, Entire extremal solutions for elliptic inclusions of Clarke′s gradient type, Z. Anal. Anwend. 29 (2010), no. 1, 63–75. Preprint   Journal   
  106. S. Carl, P. Winkert, General comparison principle for variational-hemivariational inequalities, J. Inequal. Appl. 2009, Art. ID 184348, 29 pp. Preprint   Journal   
  107. P. Brückmann, P. Winkert, T-symmetrical tensor differential forms with logarithmic poles along a hypersurface section, Int. J. Pure Appl. Math. 46 (2008), no. 1, 111–136. Preprint   Journal   
  108. P. Winkert, Discontinuous variational-hemivariational inequalities involving the p-Laplacian, J. Inequal. Appl. 2007, Art. ID 13579, 11 pp. Preprint   Journal   
Book Contributions
  1. D. Motreanu, P. Winkert, Elliptic problems with nonhomogeneous differential operators and multiple solutions, Chapter 15 in: Mathematics Without Boundaries (Surveys in Pure Mathematics), 357–379, Springer, New York, 2014. PDF   Book chapter
  2. D. Motreanu, P. Winkert, The Fucik spectrum for the negative p-Laplacian with different boundary conditions, Chapter 28 in: Nonlinear Analysis (Stability, Approximation, and Inequalities), 471–485, Springer, New York, 2012. PDF   Book chapter
Theses
  1. P. Winkert, Global a priori bounds and multiplicity results for quasilinear elliptic equations and inequalities, Habilitation thesis, Technische Universität Berlin, Berlin, Germany, November 2015. PDF
  2. P. Winkert, Comparison principles and multiple solutions for nonlinear elliptic problems, PhD thesis, Martin-Luther-Universität Halle-Wittenberg, Halle, Germany, July 2009. PDF
  3. P. Winkert, T-symmetrische Tensor-Differentialformen mit logarithmischen Polen, Diploma thesis, Martin-Luther-Universität Halle-Wittenberg, Halle, Germany, July 2006 (available only in German).
Patrick Winkert
Teaching
Teaching Experience
  • Fall 2024
    • Lectures 'Analysis I und Lineare Algebra für Ingenieurwissenschaften'
  • Spring 2024
    • Lectures 'Analysis I und Lineare Algebra für Ingenieurwissenschaften'
    • Lectures 'Analysis II für Ingenieurwissenschaften'
  • Fall 2023
    • Lectures 'Analysis II für Ingenieurwissenschaften'
  • Spring 2023
    • Lectures 'Analysis I und Lineare Algebra für Ingenieurwissenschaften'
    • Lectures 'Analysis II für Ingenieurwissenschaften'
  • Fall 2022
    • Lectures 'Analysis III für Mathematikerinnen und Mathematiker'
    • Lectures 'Analysis I und Lineare Algebra für Ingenieurwissenschaften'
  • Spring 2022
    • Lectures 'Analysis II für Mathematikerinnen und Mathematiker'
  • Fall 2021
    • Lectures 'Analysis I für Mathematikerinnen und Mathematiker'
    • Lectures 'Analysis I und Lineare Algebra für Ingenieurwissenschaften'
  • Spring 2021
    • Lectures 'Analysis I und Lineare Algebra für Ingenieurwissenschaften'
    • Lectures 'Analysis II für Ingenieurwissenschaften'
    • Seminar 'Differentialgleichungen' (with E. Emmrich)
  • Fall 2020
    • Lectures 'Analysis I und Lineare Algebra für Ingenieurwissenschaften'
  • Spring 2020
    • Lectures 'Lineare Algebra für Ingenieurwissenschaften'
    • Lectures 'Analysis I und Lineare Algebra für Ingenieurwissenschaften'
    • Seminar 'Differentialgleichungen' (with H.-C. Kreusler)
  • Fall 2019
    • Lectures 'Analysis I für Ingenieurwissenschaften'
    • Lectures 'Analysis I und Lineare Algebra für Ingenieurwissenschaften'
  • Spring 2019
    • Lectures 'Analysis I für Ingenieurwissenschaften'
    • Tutorials 'Lineare Algebra für Ingenieurwissenschaften'
    • Seminar 'Differentialgleichungen' (with H.-C. Kreusler and R. Kruse)
  • Fall 2018
    • Lectures 'Analysis I für Ingenieurwissenschaften'
    • Tutorials 'Lineare Algebra für Ingenieurwissenschaften'
  • Spring 2018
    • Lectures 'Lineare Algebra für Ingenieurwissenschaften'
    • Tutorials 'Lineare Algebra für Ingenieurwissenschaften'
  • Fall 2017
    • Lectures 'Funktionalanalysis' (MLU Halle)
    • Lectures 'Partielle Differentialgleichungen' (MLU Halle)
    • Lectures 'Lineare Algebra für Ingenieurwissenschaften'
  • Spring 2017
    • Lectures 'Lineare Algebra und Analytische Geometrie II' (HU Berlin)
    • Tutorials 'Lineare Algebra und Analytische Geometrie II' (HU Berlin)
  • Fall 2016
    • Lectures 'Funktionalanalysis' (MLU Halle)
    • Lectures 'Dynamische Systeme' (MLU Halle)
    • Tutorials 'Dynamische Systeme' (MLU Halle)
    • Seminar 'Fachseminar Analysis' (with S. Carl, MLU Halle)
    • Lectures 'Lineare Algebra für Ingenieurwissenschaften'
  • Spring 2016
    • Lectures 'Maßtheorie' (MLU Halle)
    • Lectures 'Partielle Differentialgleichungen' (MLU Halle)
  • Fall 2015
    • Lectures 'Lineare Algebra für Ingenieurwissenschaften'
    • Tutorials 'Lineare Algebra für Ingenieurwissenschaften'
  • Spring 2015
    • Tutorials 'Lineare Algebra für Ingenieurwissenschaften'
  • Fall 2014
    • Tutorials 'Analysis I für Ingenieurwissenschaften'
  • Spring 2014
    • Tutorials 'Lineare Algebra für Ingenieurwissenschaften'
  • Fall 2013
    • Tutorials 'Lineare Algebra für Ingenieurwissenschaften'
  • Spring 2013
    • Tutorials 'Lineare Algebra für Ingenieurwissenschaften'
  • Fall 2011
    • Lectures 'Funktionalanalysis II'
    • Spring 2011
    • Lectures 'Funktionalanalysis I'
    Fall 2008
    • Tutorials 'Analysis I' (MLU Halle)
Patrick Winkert
Research
Research Interests
  • A priori bounds for elliptic and parabolic problems (equations and inequalities)
  • Comparison principles and multiple solutions for nonlinear elliptic problems
  • Isotropic and anisotropic double phase problems
  • Fucik spectrum of elliptic operators
  • Gradient dependence on the right-hand side (convection term)
  • Morse theory and critical groups
  • Nonhomogeneous operators
  • Nonlinear elliptic and parabolic differential equations and inclusion
  • Nonsmooth variational problems (variational- and hemivariational inequalities)
  • Singular problems
Patrick Winkert
Editorial Activities
Member of the Editorial Board of the following journals:
Guest Editor:
Patrick Winkert
Supervision
Supervised PhD Theses
  • Ángel Crespo Blanco, Double phase elliptic problems: existence and multiplicity results, TU Berlin, September 2024.
Supervised Master Theses
  1. Singular double phase Kirchhoff problems with nonlinear Neumann boundary condition, TU Berlin, August 2024.
  2. Existence results for double phase problems via the Nehari manifold, TU Berlin, July 2021.
  3. Constant-sign and sign-changing solutions for nonlinear elliptic equations, TU Berlin, December 2020.
  4. Existenz von Lösungen für quasilineare elliptische Gleichungen mit gradientenabhängigen rechten Seiten, TU Berlin, June 2019.
  5. Lösbarkeit von Variations-Hemivariationsungleichungen mit Hilfe von Ober- und Unterlösung, TU Berlin, April 2016.
Supervised Bachelor Theses
  1. Existenz und Eindeutigkeit für quasilineare elliptische Systeme mit gekoppelten gradientenabhängigen rechten Seiten, TU Berlin, April 2023.
  2. Existenz von Lösungen bei Double-Phase-Problemen mittels kritischer Punkttheorie, TU Berlin, September 2021.
  3. Die Theorie des Bochner-Integrals, TU Berlin, August 2021.
  4. Die Methode von schwacher Ober- und Unterlösung für semilineare, elliptische Randwertprobleme, TU Berlin, January 2021.
  5. Die Nehari-Mannigfaltigkeit zur Lösung einer elliptischen Differentialgleichung, TU Berlin, July 2020.
  6. Der p-Laplace-Operator – Eigenschaften und Lösbarkeit zugehöriger Gleichungen, TU Berlin, January 2020.
  7. Lebesgue- und Sobolev-Räume mit variablen Exponenten, TU Berlin, September 2019.
  8. Origami: Definition in einem analytischen Kontext und Lösen spezieller Dirichlet-Probleme, MLU Halle, June 2018.
  9. Nonlinear eigenvalue problems for nonhomogeneous differential operators, MLU Halle, October 2017.
  10. Die Gelfandsche Darstellungstheorie, MLU Halle, May 2017.
  11. Das Fučík-Spektrum des p-Laplace-Operators mit Steklov-Randbedingung, TU Berlin, May 2016.
  12. De Giorgi-Iteration für quasilineare, elliptische Gleichungen mit Neumann-Randbedingung, TU Berlin, December 2015.
  13. The eigenvalue problem of the p-Laplacian with Robin boundary condition, TU Berlin, February 2013.
  14. Die Methode von Ober- und Unterlösung für nichtlineare, elliptische Gleichungen, TU Berlin, February 2013.
  15. A priori bounds for elliptic problems with nonlinear boundary condition, TU Berlin, June 2012.

Patrick Winkert
Imprint
Site Notice
  • Information provided according to Sec. 5 German Telemedia Act (TMG):
    • Patrick Winkert
  • Contact
    • Phone: +49 (0) 30 314 - 2 39 74
      Email: patrick(at)winkert.de
  • Dispute resolution
    • The European Commission provides a platform for online dispute resolution (OS): https://ec.europa.eu/consumers/odr.
      We do not take part in online dispute resolutions at consumer arbitration boards.
  • Liability for Contents
    • As service providers, we are liable for own contents of these websites according to Sec. 7, paragraph 1 German Telemedia Act (TMG). However, according to Sec. 8 to 10 German Telemedia Act (TMG), service providers are not obligated to permanently monitor submitted or stored information or to search for evidences that indicate illegal activities. Legal obligations to removing information or to blocking the use of information remain unchallenged. In this case, liability is only possible at the time of knowledge about a specific violation of law. Illegal contents will be removed immediately at the time we get knowledge of them.
  • Liability for Links
    • Our offer includes links to external third party websites. We have no influence on the contents of those websites, therefore we cannot guarantee for those contents. Providers or administrators of linked websites are always responsible for their own contents. The linked websites had been checked for possible violations of law at the time of the establishment of the link. Illegal contents were not detected at the time of the linking. A permanent monitoring of the contents of linked websites cannot be imposed without reasonable indications that there has been a violation of law. Illegal links will be removed immediately at the time we get knowledge of them.
  • Copyright
    • Contents and compilations published on these websites by the providers are subject to German copyright laws. Reproduction, editing, distribution as well as the use of any kind outside the scope of the copyright law require a written permission of the author or originator. Downloads and copies of these websites are permitted for private use only. The commercial use of our contents without permission of the originator is prohibited. Copyright laws of third parties are respected as long as the contents on these websites do not originate from the provider. Contributions of third parties on this site are indicated as such. However, if you notice any violations of copyright law, please inform us. Such contents will be removed immediately.
Privacy Policy

1 An overview of data protection
  • General
    • The following gives a simple overview of what happens to your personal information when you visit our website. Personal information is any data with which you could be personally identified. Detailed information on the subject of data protection can be found in our privacy policy found below.
Data collection on our website
  • Who is responsible for the data collection on this website?
    • The data collected on this website are processed by the website operator. The operator's contact details can be found in the website's required legal notice.
  • How do we collect your data?
    • Some data are collected when you provide it to us. This could, for example, be data you enter on a contact form. Other data are collected automatically by our IT systems when you visit the website. These data are primarily technical data such as the browser and operating system you are using or when you accessed the page. These data are collected automatically as soon as you enter our website.
  • What do we use your data for?
    • Part of the data is collected to ensure the proper functioning of the website. Other data can be used to analyze how visitors use the site.
  • What rights do you have regarding your data?
    • You always have the right to request information about your stored data, its origin, its recipients, and the purpose of its collection at no charge. You also have the right to request that it be corrected, blocked, or deleted. You can contact us at any time using the address given in the legal notice if you have further questions about the issue of privacy and data protection. You may also, of course, file a complaint with the competent regulatory authorities.
2 General information and mandatory information
  • Data protection
    • The operators of this website take the protection of your personal data very seriously. We treat your personal data as confidential and in accordance with the statutory data protection regulations and this privacy policy. If you use this website, various pieces of personal data will be collected. Personal information is any data with which you could be personally identified. This privacy policy explains what information we collect and what we use it for. It also explains how and for what purpose this happens. Please note that data transmitted via the internet (e.g. via email communication) may be subject to security breaches. Complete protection of your data from third-party access is not possible.
  • Notice concerning the party responsible for this website
    • The party responsible for processing data on this website is:
      Patrick Winkert

      Phone: +49 (0) 30 314 - 2 39 74
      Email: patrick(at)winkert.de

      The responsible party is the natural or legal person who alone or jointly with others decides on the purposes and means of processing personal data (names, email addresses, etc.).
  • Revocation of your consent to the processing of your data
    • Many data processing operations are only possible with your express consent. You may revoke your consent at any time with future effect. An informal email making this request is sufficient. The data processed before we receive your request may still be legally processed.
  • Right to file complaints with regulatory authorities
    • If there has been a breach of data protection legislation, the person affected may file a complaint with the competent regulatory authorities. The competent regulatory authority for matters related to data protection legislation is the data protection officer of the German state in which our company is headquartered. A list of data protection officers and their contact details can be found at the following link: https://www.bfdi.bund.de/DE/Infothek/Anschriften_Links/anschriften_links-node.html.
  • Right to data portability
    • You have the right to have data which we process based on your consent or in fulfillment of a contract automatically delivered to yourself or to a third party in a standard, machine-readable format. If you require the direct transfer of data to another responsible party, this will only be done to the extent technically feasible.
  • Information, blocking, deletion
    • As permitted by law, you have the right to be provided at any time with information free of charge about any of your personal data that is stored as well as its origin, the recipient and the purpose for which it has been processed. You also have the right to have this data corrected, blocked or deleted. You can contact us at any time using the address given in our legal notice if you have further questions on the topic of personal data.
  • Opposition to promotional emails
    • We hereby expressly prohibit the use of contact data published in the context of website legal notice requirements with regard to sending promotional and informational materials not expressly requested. The website operator reserves the right to take specific legal action if unsolicited advertising material, such as email spam, is received.
3 Data collection on our website
  • Server log files
    • The website provider automatically collects and stores information that your browser automatically transmits to us in "server log files". These are:

      - Browser type and browser version
      - Operating system used
      - Referrer URL
      - Host name of the accessing computer
      - Time of the server request
      - IP address

      These data will not be combined with data from other sources. The basis for data processing is Art. 6 (1) (f) DSGVO, which allows the processing of data to fulfill a contract or for measures preliminary to a contract.