dr hab. Jarosław Mederski, prof. IM PAN

 Associate Professor at Institute of Mathematics
 Polish Academy of Sciences
 ul. Śniadeckich 8, 00-656 Warsaw, Poland
  jmederski at impan dot pl
  MathSciNet Google Scholar
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Seminar Variational Methods and PDEs
Research interests:
Short CV:
Grant NCN SONATA BIS: Nonlinear equations involving the curl-curl operator, 08.2018-07.2023
The local co-investigators involved in the project:
Publications:
  1. P. d'Avenia, J. Mederski, A. Pomponio: Nonlinear scalar field equation with competing nonlocal terms,
    submitted arXiv:2010.13184
  2. M. Gaczkowski, J. Mederski, J.Schino: Multiple solutions to cylindrically symmetric curl-curl problems and related Schrödinger equations with singular potentials,
    submitted arXiv:2006.03565
  3. B. Bieganowski, J. Mederski: Normalized ground states of the nonlinear Schrödinger equation with at least mass critical growth,
    submitted arXiv:2002.08344
  4. J. Mederski, A. Szulkin: Sharp constant in the curl inequality and ground states for curl-curl problem with critical exponent,
    submitted arXiv:2002.00613
  5. B. Bieganowski, J. Mederski: Bound states for the Schrödinger equation with mixed-type nonlinearites,
    submitted arXiv:1905.04542
  6. J. Mederski, J. Schino, A. Szulkin: Multiple solutions to a nonlinear curl-curl problem in R^3,
    Arch. Rational Mech. Anal. 236 (2020) 253-288 DOI 10.1007/s00205-019-01469-3 arXiv:1901.05776
  7. J. Mederski: General class of optimal Sobolev inequalities and nonlinear scalar field equations,
    submitted arXiv:1812.11451
  8. B. Bieganowski, J. Mederski: Note on semiclassical states for the Schrödinger equation with nonautonomous nonlinearities,
    Appl. Math. Lett. 88 (2019), 149-155, arXiv:1808.09148
  9. J. Mederski: Nonradial solutions of nonlinear scalar field equations,
    Nonlinearity 33 (2020), 6349-6380, doi:10.1088/1361-6544/aba889 arXiv:1711.05711
  10. J. Mederski: Nonlinear time-harmonic Maxwell equations in a bounded domain: lack of compactness,
    survey, Sci. China Math. 61 (2018), no. 11, 1963-1970 doi.org/10.1007/s11425-017-9312-8
  11. T. Bartsch, J. Mederski: Nonlinear time-harmonic Maxwell equations in domains,
    J. Fixed Point Theory Appl. 19 (2017), no. 1, 959-986 DOI 10.1007/s11784-017-0409-1 (the special issue in honour of Prof. Paul Rabinowitz) arXiv:1610.06338
  12. J. Mederski: The Brezis-Nirenberg problem for the curl-curl operator,
    J. Funct. Anal. 274 (5), (2018), 1345-1380 DOI 10.1016/j.jfa.2017.12.012 arXiv:1609.03989
  13. P. d'Avenia, J. Mederski, A. Pomponio: Vortex ground states for Klein-Gordon-Maxwell-Proca type systems,
    J. Math. Phys. 58 (2017), no. 4, 041503, 19 pp., DOI 10.1063/1.4982038 arXiv:1603.04649
  14. B. Bieganowski, J. Mederski: Nonlinear Schrödinger equations with sum of periodic and vanishig potentials and sign-changning nonlinearities,
    Communications on Pure and Applied Analysis 17(1) (2018)143-161, DOI 10.3934/cpaa.2018009, arXiv:1602.05078
  15. T. Bartsch, J. Mederski: Nonlinear time-harmonic Maxwell equations in an anisotropic bounded medium,
    J. Funct. Anal. 272 (2017), no. 10, 4304-4333 DOI 10.1016/j.jfa.2017.02.019 arXiv:1509.01994
  16. J. Mederski: Nonlinear time-harmonic Maxwell equations in R^3: recent results and open questions,
    Lecture Notes of Seminario Interdisciplinare di Matematica Vol. 13 (2016), 47–57 link
  17. Q. Guo, J. Mederski: Ground states of nonlinear Schrödinger equations with sum of periodic and inverse-square potentials,
    J. Differential Equations 260 (2016), no. 5, 4180–4202 DOI 10.1016/j.jde.2015.11.006 arXiv:1412.6022
  18. J. Mederski: Ground states of a system of nonlinear Schrödinger equations with periodic potentials,
    Comm. Partial Differential Equations 41 (2016), no. 9, 1426–1440 DOI 10.1080/03605302.2016.1209520 arXiv:1411.5582
  19. J. Mederski: Ground states of time-harmonic semilinear Maxwell equations in R^3 with vanishing permittivity,
    Arch. Rational Mech. Anal., 218 (2), (2015), 825-861 DOI 10.1007/s00205-015-0870-1 arXiv:1406.4535
  20. P. d'Avenia, J. Mederski: Positive ground states for a system of Schrödinger equations with critically growing nonlinearities,
    Calc. Var. Partial Differential Equations 53 (2015), no. 3-4, 879–900 DOI 10.1007/s00526-014-0770-5 arXiv:1403.3211
  21. T. Bartsch, J. Mederski: Ground and Bound State Solutions of Semilinear Time-Harmonic Maxwell Equations in a Bounded Domain,
    Arch. Rational Mech. Anal. 215 (1), (2015), 283-306 DOI 10.1007/s00205-014-0778-1 arXiv:1310.4731
  22. J. Mederski: Solutions to a nonlinear Schrödinger equation with periodic potential and zero on the boundary of the spectrum,
    Topol. Methods Nonlinear Anal. 46 (2015), no. 2, 755–771 arXiv:1308.4320
  23. J. Mederski: Vietoris-Begle theorems for nonclosed maps,
    Topol. Methods Nonlinear Anal. 41 (2013), no. 1, 191-205.
  24. J. Mederski: Graph approximations of set-valued maps under constraints,
    Topol. Methods Nonlinear Anal. 39 (2012), no. 2, 361-389.
  25. J. Mederski: Equilibria of nonconvex valued maps under constraints,
    J. Math. Anal. Appl. 389 (2012), no. 2, 701-704.
  26. J. Mederski: Fiberwise absolute neighborhood extensors for a class of metrizable spaces,
    Topology Appl. 156 (2009), no. 13, 2295-2305.
  27. J. Mederski, Ł. Mikulski, P. Bała: Asynchronous Parallel Molecular Dynamics Simulations,
    Parallel Processing and Applied Mathematics, Lecture Notes in Computer Science Volume 4967 (2008), pp 439-446.
  28. W. Kryszewski, J. Mederski: Fixed point index for Krasnoselskii-type set-valued maps on complete ANRs,
    Topol. Methods Nonlinear Anal. 28 (2006), no. 2, 335-384.
Teaching mathematical analysis, pdes, financial and actuarial mathematics, SQL and databases - Oracle, C++ programming:
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