Patrick Winkert

patrick_winkert
 


 




 
Technische Universität Berlin
Institut für Mathematik
Sekretariat MA 1-0
MA 418
Straße des 17. Juni 136
10623 Berlin, Germany

+49 - 30 - 314 - 2 74 87
+49 - 30 - 314 - 2 89 67

winkert(at)math.tu-berlin.de
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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
    Reviewers: Prof. Dr. Etienne Emmrich (TU Berlin), Prof. Dr. Siegfried Carl (University of Halle), Prof. Dr. Salvatore A. Marano (University of Catania), Prof. Dr. Kanishka Perera (Florida Institute of Technology, Melbourne)
  • 2009: Ph.D. in Mathematics (Dr.rer.nat.), Thesis: Comparison principles and multiple solutions for nonlinear elliptic problems, Thesis Supervisor: Prof. Dr. Siegfried Carl, Martin-Luther-Universität Halle-Wittenberg, Halle, Germany
  • 2006: Master in Mathematics (Diploma in Mathematics), Thesis: T-symmetrische Tensor-Differentialformen mit logarithmischen Polen, Thesis Supervisior: Prof. Dr. Klaus Peter Brückmann, Martin-Luther-Universität Halle-Wittenberg, Halle, Germany
Employment
  • since 2019: Lecturer (tenured) & Research Assistant, 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
  • 2008 – 2009: Research Assistant, Martin-Luther-Universität Halle-Wittenberg, Halle, Germany
  • 2006 – 2008: Ph.D. Student, Martin-Luther-Universität Halle-Wittenberg, Halle, Germany
Awards
  • 2007: Promotion price, awarded by the Georg Cantor Society for the diploma (master) in mathematics
  • 2006 – 2008: Graduate scholarship assigned by the federal state Sachsen-Anhalt
  • 2006: Award of the German Mathematical Society for course achievement
  • 2003: Awarded by the German Mathematical Society for the intermediate diploma in mathematics
Patrick Winkert
Publications

Monographs
  1. N. S. Papageorgiou, P. Winkert, Applied Nonlinear Functional Analysis. An Introduction, De Gruyter, Berlin, 2018, x+612 pp.
    De Gruyter
Preprints
  1. C. Farkas, A. Fiscella, P. Winkert, Singular Finsler double phase problems with nonlinear boundary condition, 2021. arXiv
  2. N. S. Papageorgiou, P. Winkert, Positive solutions for singular anisotropic (p,q)-equations, 2021. arXiv
  3. W. Liu, G. Dai, N. S. Papageorgiou, P. Winkert, Existence of solutions for singular double phase problems via the Nehari manifold method, 2021. arXiv
  4. S. El Manouni, G. Marino, P. Winkert, Existence results for double phase problems depending on Robin and Steklov eigenvalues for the p-Laplacian, 2020. arXiv
  5. C. Farkas, P. Winkert, An existence result for singular Finsler double phase problems, 2020. arXiv
  6. 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, 2020. arXiv
  7. N. S. Papageorgiou, P. Winkert, Existence and nonexistence of positive solutions for singular (p,q)-equations with superdiffusive perturbation, 2020. arXiv
  8. N. S. Papageorgiou, P. Winkert, On a class of singular anisotropic (p,q)-equations, 2020. arXiv
Refereed Articles
  1. 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
  2. N. S. Papageorgiou, P. Winkert, Singular Dirichlet (p,q)-equations, Mediterr. J. Math., accepted 2020. Preprint   Journal   arXiv
  3. 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   
  4. 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., accepted 2020. Preprint   Journal   
  5. N. S. Papageorgiou, P. Winkert, (p,q)-Equations with singular and concave convex nonlinearities, Appl. Math. Optim., accepted 2020. Preprint   Journal   arXiv
  6. S. Zeng, L. Gasiński, P. Winkert, Y. Bai, Existence of solutions for double phase obstacle problems with multivalued convection term, J. Math. Anal. Appl., accepted 2020. Preprint   Journal   
  7. N. S. Papageorgiou, P. Winkert, Positive solutions for weighted singular p-Laplace equations via Nehari manifolds, Appl. Anal., accepted 2019. Preprint   Journal   arXiv
  8. 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   
  9. 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
  10. 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, 176. Preprint   Journal   
  11. 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
  12. 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   
  13. 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
  14. L. Gasiński, P. Winkert, Constant sign solutions for double phase problems with superlinear nonlinearity, Nonlinear Anal. 195 (2020), 111739, 9 pp. Preprint   Journal   arXiv
  15. 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   
  16. 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
  17. 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
  18. 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   
  19. 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   
  20. 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   
  21. 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   
  22. D. Motreanu, P. Winkert, Existence and asymptotic properties for quasilinear elliptic equations with gradient dependence, Appl. Math. Lett. 95 (2019), 78–84. Preprint   Journal   
  23. N. S. Papageorgiou, P. Winkert, Nonlinear systems with Hartman-type perturbations, Monatsh. Math. 190 (2019), no. 2, 389–404. Preprint   Journal   
  24. 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
  25. N. S. Papageorgiou, P. Winkert, Solutions with sign information for nonlinear nonhomogeneous problems, Math. Nachr. 292 (2019), no. 4, 871–891. Preprint   Journal   
  26. N. S. Papageorgiou, P. Winkert, Singular p-Laplacian equations with superlinear perturbation, J. Differential Equations 266 (2019), no. 2-3, 1462–1487. Preprint   Journal   
  27. 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   
  28. N. S. Papageorgiou, P. Winkert, Asymmetric (p,2)-equations, superlinear at +∞, resonant at -∞, Bull. Sci. Math. 141 (2017), no. 5, 443–488. Preprint   Journal   
  29. S. El Manouni, H. Hajaiej, P. Winkert, Bounded solutions to nonlinear problems in RN involving the fractional Laplacian depending on parameters, Minimax Theory and Its Applications 2 (2017), no. 2, 265–283. Preprint   Journal   arXiv
  30. 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   
  31. 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
  32. 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   
  33. G. Bonanno, G. D'Aguì, P. Winkert, Sturm-Liouville equations involving discontinuous nonlinearities, Minimax Theory and Its Applications 1 (2016), no. 1, 125–143. Preprint   Journal   
  34. N. S. Papageorgiou, P. Winkert, Nonlinear nonhomogeneous Dirichlet equations with a superlinear nonlinearity, Results Math. 70 (2016), no. 1, 31–79. Preprint   Journal   arXiv
  35. 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
  36. 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   
  37. N. S. Papageorgiou, P. Winkert, Resonant (p,2)-equations with concave terms, Appl. Anal. 94 (2015), no. 2, 342–360. Preprint   Journal   
  38. P. Winkert, On the boundedness of solutions to elliptic variational inequalities, Set-Valued Var. Anal. 22 (2014), no. 4, 763–781. Preprint   Journal   
  39. 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   
  40. 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   
  41. 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   
  42. 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   
  43. 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
  44. 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   
  45. 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   
  46. 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   
  47. D. Motreanu, P. Winkert, Variational-hemivariational inequalities with nonhomogeneous Neumann boundary condition, Matematiche (Catania) 65 (2010), no. 2, 109–119. Preprint   Journal   
  48. 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   
  49. P. Winkert, Local C1-minimizers versus local W1,p-minimizers of nonsmooth functionals, Nonlinear Anal. 72 (2010), no. 11, 4298–4303. Preprint   Journal   
  50. P. Winkert, L-estimates for nonlinear elliptic Neumann boundary value problems, NoDEA Nonlinear Differential Equations Appl. 17 (2010), no. 3, 289–302. Preprint   Journal   
  51. 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   
  52. P. Winkert, Entire extremal solutions for elliptic inclusions of Clarke′s gradient type, Z. Anal. Anwend. 29 (2010), no. 1, 63–75. Preprint   Journal   
  53. S. Carl, P. Winkert, General comparison principle for variational-hemivariational inequalities, J. Inequal. Appl. 2009, Art. ID 184348, 29 pp. Preprint   Journal   
  54. 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   
  55. 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
Unpublished Manuscripts
  1. P. Winkert, Local minimizers of functionals in variable exponent Sobolev spaces, 8pp., 2011.
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
  • Spring 2021
    • Lectures 'Analysis I und Lineare Algebra für Ingenieurwissenschaften'
    • Lectures 'Analysis II für Ingenieurwissenschaften'
  • 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 C. H. 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 C.H. 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 Work

Member of the Editorial Board of the following journals:
Patrick Winkert
Supervision

Supervised Master Theses
  1. Existence results for double phase problems via the Nehari manifold, TU Berlin, in preparation.
  2. Constant-sign and sign-changing solutions for nonlinear elliptic equations, TU Berlin, December 2020.
  3. Existenz von Lösungen für quasilineare elliptische Gleichungen mit gradientenabhängigen rechten Seiten, TU Berlin, June 2019.
  4. Lösbarkeit von Variations-Hemivariationsungleichungen mit Hilfe von Ober- und Unterlösung, TU Berlin, April 2016.
Supervised Bachelor Theses
  1. Existenz von Lösungen bei Double-Phase-Problemen mittels kritischer Punkttheorie, TU Berlin, in preparation.
  2. Die Theorie des Bochner-Integrals, TU Berlin, in preparation.
  3. Die Methode von schwacher Ober- und Unterlösung für semilineare, elliptische Randwertprobleme, TU Berlin, January 2021.
  4. Die Nehari-Mannigfaltigkeit zur Lösung einer elliptischen Differentialgleichung, TU Berlin, July 2020.
  5. Der p-Laplace-Operator – Eigenschaften und Lösbarkeit zugehöriger Gleichungen, TU Berlin, January 2020.
  6. Lebesgue- und Sobolev-Räume mit variablen Exponenten, TU Berlin, September 2019.
  7. Origami: Definition in einem analytischen Kontext und Lösen spezieller Dirichlet-Probleme, MLU Halle, June 2018.
  8. Nonlinear eigenvalue problems for nonhomogeneous differential operators, MLU Halle, October 2017.
  9. Die Gelfandsche Darstellungstheorie, MLU Halle, May 2017.
  10. Das Fučík-Spektrum des p-Laplace-Operators mit Steklov-Randbedingung, TU Berlin, May 2016.
  11. De Giorgi-Iteration für quasilineare, elliptische Gleichungen mit Neumann-Randbedingung, TU Berlin, December 2015.
  12. The eigenvalue problem of the p-Laplacian with Robin boundary condition, TU Berlin, February 2013.
  13. Die Methode von Ober- und Unterlösung für nichtlineare, elliptische Gleichungen, TU Berlin, February 2013.
  14. A priori bounds for elliptic problems with nonlinear boundary condition, TU Berlin, June 2012.

Patrick Winkert
Imprint

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