Research Assistants (tenured)

Priv.-Doz. Dr.

Patrick Winkert

winkert@math.tu-berlin.de

+49 30 314-27487

Organization name Institute of Mathematics
Office MA 1-0
Room MA 418
Address Straße des 17. Juni 136
10623 Berlin

Curriculum Vitae

Academic Degrees

2015Habilitation in Mathematics, TU Berlin
2009PhD in Mathematics, MLU Halle-Wittenberg
2006Master in Mathematics, MLU Halle-Wittenberg

Employment History

since 2019Lecturer (tenured) and Research Assistant, TU Berlin
since 2016Privatdozent, TU Berlin
Fall 17Substitute Professor (Analysis), MLU Halle-Wittenberg
Spring 17Guest Professor (Angewandte Analysis), HU Berlin
Fall 16Substitute Professor (Analysis), MLU Halle-Wittenberg
Spring 16Substitute Professor (Angewandte Analysis), MLU Halle-Wittenberg
2009-2019Research Assistant, TU Berlin
2006-2009Research Assistant, MLU Halle-Wittenberg

Teaching

Lectures

Spring 23Analysis I und Lineare Algebra für Ingenieurwissenschaften
 Analysis II für Ingenieurwissenschaften
Fall 22Analysis III für Mathematikerinnen und Mathematiker
 Analysis I und Lineare Algebra für Ingenieurwissenschaften
Spring 22Analysis II für Mathematikerinnen und Mathematiker
Fall 21Analysis I für Mathematikerinnen und Mathematiker
 Analysis I und Lineare Algebra für Ingenieurwissenschaften
Spring 21Analysis I und Lineare Algebra für Ingenieurwissenschaften
 Analysis II für Ingenieurwissenschaften
Fall 20Analysis I und Lineare Algebra für Ingenieurwissenschaften
Spring 20Analysis I und Lineare Algebra für Ingenieurwissenschaften
 Lineare Algebra für Ingenieurwissenschaften
Fall 19Analysis I und Lineare Algebra für Ingenieurwissenschaften
 Analysis I für Ingenieurwissenschaften
Spring 19Analysis I für Ingenieurwissenschaften
Fall 18Analysis I für Ingenieurwissenschaften
Spring 18Lineare Algebra für Ingenieurwissenschaften
Fall 17Funktionalanalysis (University of Halle)
 Partielle Differentialgleichungen (University of Halle)
 Lineare Algebra für Ingenieurwissenschaften
Spring 17Lineare Algebra und Analytische Geometrie II (HU Berlin)
Fall 16Funktionalanalysis (University of Halle)
 Dynamische Systeme (University of Halle)
 Lineare Algebra für Ingenieurwissenschaften
Spring 16Maßtheorie (University of Halle)
 Partielle Differentialgleichungen (University of Halle)
Fall 15Lineare Algebra für Ingenieurwissenschaften
Fall 11Funktionalanalysis II
Spring 11Funktionalanalysis I

Seminars

Spring 21Differentialgleichungen (with E. Emmrich)
Spring 20Differentialgleichungen (with H.-C. Kreusler)
Spring 19Differentialgleichungen (with H.-C. Kreusler and R. Kruse)
Fall 16Fachseminar Analysis (University of Halle, with S. Carl)

Tutorials

Spring 19Lineare Algebra für Ingenieurwissenschaften
Fall 18Lineare Algebra für Ingenieurwissenschaften
Spring 18Lineare Algebra für Ingenieurwissenschaften
Spring 17Lineare Algebra und Analytische Geometrie II (HU Berlin)
Fall 16Dynamische Systeme (University of Halle)
Fall 15Lineare Algebra für Ingenieurwissenschaften
Spring 15Lineare Algebra für Ingenieurwissenschaften
Fall 14Analysis I für Ingenieurwissenschaften
Spring 14Lineare Algebra für Ingenieurwissenschaften
Fall 13Lineare Algebra für Ingenieurwissenschaften
Spring 13Lineare Algebra für Ingenieurwissenschaften
Fall 08Analysis I (University of Halle)

Supervision

Current PhD Projects

1.Ángel Crespo Blanco, Isotropic and anisotropic double phase problems, TU Berlin, BMS Phase II Scholarship.

Supervised Master Theses

4.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.
2.Existenz von Lösungen für quasilineare elliptische Gleichungen mit gradientenabhängigen rechten Seiten, TU Berlin, June 2019.
1.Lösbarkeit von Variations-Hemivariationsungleichungen mit Hilfe von Ober- und Unterlösung, TU Berlin, April 2016.

Supervised Bachelor Theses

15.Existenz und Eindeutigkeit für quasilineare elliptische Systeme mit gekoppelten gradientenabhängigen rechten Seiten, TU Berlin, in preparation.
14.Existenz von Lösungen bei Double-Phase-Problemen mittels kritischer Punkttheorie, TU Berlin, September 2021.
13.Die Theorie des Bochner-Integrals, TU Berlin, August 2021.
12.Die Methode von schwacher Ober- und Unterlösung für semilineare, elliptische Randwertprobleme, TU Berlin, January 2021.
11.Die Nehari-Mannigfaltigkeit zur Lösung einer elliptischen Differentialgleichung, TU Berlin, July 2020.
10.Der p-Laplace-Operator – Eigenschaften und Lösbarkeit zugehöriger Gleichungen, TU Berlin, January 2020.
9.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.
7.Nonlinear eigenvalue problems for nonhomogeneous differential operators, MLU Halle, October 2017.
6.Die Gelfandsche Darstellungstheorie, MLU Halle, May 2017.
5.Das Fučík-Spektrum des p-Laplace-Operators mit Steklov-Randbedingung, TU Berlin, May 2016.
4.De Giorgi-Iteration für quasilineare, elliptische Gleichungen mit Neumann-Randbedingung, TU Berlin, December 2015.
3.The eigenvalue problem of the p-Laplacian with Robin boundary condition, TU Berlin, February 2013.
2.Die Methode von Ober- und Unterlösung für nichtlineare, elliptische Gleichungen, TU Berlin, February 2013.
1.A priori bounds for elliptic problems with nonlinear boundary condition, TU Berlin, June 2012.

Research

  • 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

Editorial Activities

Publications

Monographs

1.N.S. Papageorgiou, P. Winkert, Applied Nonlinear Functional Analysis. An Introduction, De Gruyter, Berlin, 2018, x+612 pp.

Refereed Articles

82.Y. Liu, V.T. Nguyen, P. Winkert, S. Zeng, Coupled double phase obstacle systems involving nonlocal functions and multivalued convection terms, Monatsh. Math., accepted 2023.
81.A. Sciammetta, E. Tornatore, P. Winkert, Bounded weak solutions to superlinear Dirichlet double phase problems, Anal. Math. Phys., accepted 2023.
80.S. Zeng, N.S. Papageorgiou, P. Winkert, Inverse problems for double-phase obstacle problems with variable exponents, J. Optim. Theory Appl., accepted 2022.
79.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.
78.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.
77.F. Vetro, P. Winkert, Constant sign solutions for double phase problems with variable exponents, Appl. Math. Lett. 135 (2023), Paper No. 108404, 7 pp.
76.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.
75.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, accepted 2022.
74.S. Zeng, V.D. Rădulescu, P. Winkert, Double phase obstacle problems with multivalued convection and mixed boundary value conditions, Dyn. Syst. Ser. B 28 (2023), no. 2, 999–1023.
73.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.
72.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.
71.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.
70.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.
69.S. Zeng, V.D. Rădulescu, P. Winkert, Double phase obstacle problems with variable exponent, Adv. Differential Equations 27 (2022), no. 9-10, 611–645.
68.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.
67.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.
66.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.
65.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.
64.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.
63.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.
62.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.
61.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.
60.N.S. Papageorgiou, P. Winkert, On a class of singular anisotropic (p,q)-equations, Rev. Mat. Complut. 35 (2022), no. 2, 545–571.
59.C. Farkas, A. Fiscella, P. Winkert, Singular Finsler double phase problems with nonlinear boundary condition, Adv. Nonlinear Stud. 21 (2021), no. 4, 809–825.
58.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.
57.N.S. Papageorgiou, P. Winkert, Positive solutions for singular anisotropic (p,q)-equations, J. Geom. Anal. 31 (2021), no. 12, 11849–11877.
56.C. Farkas, P. Winkert, An existence result for singular Finsler double phase problems, J. Differential Equations 286 (2021), 455–473.
55.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.
54.N.S. Papageorgiou, P. Winkert, Singular Dirichlet (p,q)-equations, Mediterr. J. Math. 18 (2021), no. 4, Paper No. 141, 20 pp.
53.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.
52.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.
51.N.S. Papageorgiou, P. Winkert, (p,q)-Equations with singular and concave convex nonlinearities, Appl. Math. Optim. 84 (2021), no. 3, 2601–2628.
50.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.
49.N.S. Papageorgiou, P. Winkert, Positive solutions for weighted singular p-Laplace equations via Nehari manifolds, Appl. Anal. 100 (2021), no. 11, 2436–2448.
48.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.
47.A. Bahrouni, V.D. Rădulescu, P. Winkert, Robin fractional problems with symmetric variable growth, J. Math. Phys. 61 (2020), no. 10, 101503.
46.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.
45.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.
44.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.
43.G. Marino, P. Winkert, L∞-bounds for general singular elliptic equations with convection term, Appl. Math. Lett. 107 (2020), 106410, 6 pp.
42.L. Gasiński, P. Winkert, Constant sign solutions for double phase problems with superlinear nonlinearity, Nonlinear Anal. 195 (2020), 111739, 9 pp.
41.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.
40.L. Gasiński, P. Winkert, Existence and uniqueness results for double phase problems with convection term, J. Differential Equations 268 (2020), no. 8, 4183-4193.
39.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.
38.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.
37.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.
36.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.
35.S.A. Marano, P. Winkert, On a quasilinear elliptic problem with convection term and nonlinear boundary condition, Nonlinear Anal. 187 (2019), 159–169.
34.D. Motreanu, P. Winkert, Existence and asymptotic properties for quasilinear elliptic equations with gradient dependence, Appl. Math. Lett. 95 (2019), 78–84.
33.N.S. Papageorgiou, P. Winkert, Nonlinear systems with Hartman-type perturbations, Monatsh. Math. 190 (2019), no. 2, 389–404.
32.G. Marino, P. Winkert, Moser iteration applied to elliptic equations with critical growth on the boundary, Nonlinear Anal. 180 (2019), 154–169.
31.N.S. Papageorgiou, P. Winkert, Solutions with sign information for nonlinear nonhomogeneous problems, Math. Nachr. 292 (2019), no. 4, 871–891.
30.N.S. Papageorgiou, P. Winkert, Singular p-Laplacian equations with superlinear perturbation, J. Differential Equations 266 (2019), no. 2-3, 1462–1487.
29.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.
28.N. S. Papageorgiou, P. Winkert, Asymmetric (p,2)-equations, superlinear at +∞, resonant at -∞, Bull. Sci. Math. 141 (2017), no. 5, 443–488.
27.S. El Manouni, H. Hajaiej, P. Winkert, Nonlinear problems for the fractional Laplacian in RN involving parameters, Minimax Theory Appl. 2 (2017), no. 2, 265–283.
26.N.S. Papageorgiou, P.Winkert, Positive solutions for nonlinear nonhomogeneous Dirichlet problems with concave-convex nonlinearities, Positivity 20 (2016), no. 4, 945–979.
25.P. Winkert, R. Zacher, Global a priori bounds for weak solutions to quasilinear parabolic equations with nonstandard growth, Nonlinear Anal. 145 (2016), 1-23.
24.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.
23.G. Bonanno, G. D’Aguì, P. Winkert, Sturm-Liouville equations involving discontinuous nonlinearities, Minimax Theory Appl. 1 (2016), no. 1, 125–143.
22.N.S. Papageorgiou, P. Winkert, Nonlinear nonhomogeneous Dirichlet equations involving a superlinear nonlinearity, Results Math. 70 (2016), no. 1, 31–79.
21.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 online as note, 2015, 1–3.
20.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.
19.N.S. Papageorgiou, P. Winkert, Resonant (p; 2)-equations with concave terms, Appl. Anal. 94 (2015), no. 2, 342–360.
18.P. Winkert, On the boundedness of solutions to elliptic variational inequalities, Set-Valued Var. Anal. 22 (2014), no. 4, 763–781.
17.G. Bonanno, P. Winkert, Multiplicity results to a class of variational-hemivariational inequalities, Topol. Methods Nonlinear Anal. 43 (2014), no. 2, 493–516.
16.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.
15.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.
14.P. Winkert, Multiplicity results for a class of elliptic problems with nonlinear boundary condition, Commun. Pure Appl. Anal. 12 (2013), no. 2, 785–802.
13.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.
12.D. Motreanu, P. Winkert, On the Fučík spectrum for the p-Laplacian with Robin boundary condition, Nonlinear Anal. 74 (2011), no. 14, 4671–4681.
11.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.
10.P. Winkert, Multiple solution results for elliptic Neumann problems involving setvalued nonlinearities, J. Math. Anal. Appl. 377 (2011), no. 1, 121–134.
9.D. Motreanu, P. Winkert, Variational-hemivariational inequalities with nonhomogeneous Neumann boundary condition, Matematiche (Catania) 65 (2010), no. 2, 109–119.
8.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.
7.P. Winkert, Local C1-minimizers versus local W1,p-minimizers of nonsmooth functionals, Nonlinear Anal. 72 (2010), no. 11, 4298–4303.
6.P. Winkert, L∞-estimates for nonlinear elliptic Neumann boundary value problems, NoDEA Nonlinear Differential Equations Appl. 17 (2010), no. 3, 289–302.
5.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.
4.P. Winkert, Entire extremal solutions for elliptic inclusions of Clarke’s gradient type, Z. Anal. Anwend. 29 (2010), no. 1, 63–75.
3.S. Carl, P. Winkert, General comparison principle for variational-hemivariational inequalities, J. Inequal. Appl. 2009, Art. ID 184348, 29 pp.
2.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.
1.P. Winkert, Discontinuous variational-hemivariational inequalities involving the p-Laplacian, J. Inequal. Appl. 2007, Art. ID 13579, 11 pp.

Book Contributions

2.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.
1.D. Motreanu, P. Winkert, The Fucík 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.

Unpublished Manuscripts

1.P. Winkert, Local minimizers of functionals in variable exponent Sobolev spaces, 8pp., 2011.

Theses

3.P. Winkert, Global a priori bounds and multiplicity results for quasilinear elliptic equations and inequalities, Habilitation thesis, Technische Universität Berlin, December 2015.
2.P. Winkert, Comparison principles and multiple solutions for nonlinear elliptic problems, PhD thesis, Martin-Luther-Universität Halle-Wittenberg, July 2009.
1.P. Winkert, T-symmetrische Tensor-Differentialformen mit logarithmischen Polen, Diploma (Master) thesis, Martin-Luther-Universität Halle-Wittenberg, July 2006.