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
[Home] [Research interests] [Short CV] [SONATA BIS project] [OPUS project] [Publications] [Teaching] [Other]
Seminar Variational Methods and PDEs
Research interests:
Short CV:
Grant NCN SONATA BIS: Nonlinear equations involving the curl-curl operator, 08.2018-07.2023, PI: Jarosław Mederski
The local co-investigators involved in the project:
Grant NCN OPUS: Analysis of travelling waves in semilinear elliptic problems, 01.2021-1.2023, PI: Jarosław Mederski
Publications:
  1. J. Mederski, A. Szulkin: Multiple normalized solutions to a system of nonlinear Schrödinger equations,
    submitted arXiv:2403.16987
  2. P. d'Avenia, J. Mederski: Between Maxwell and Born-Infeld: the presence of the magnetic field,
    submitted arXiv:2403.08924
  3. L. Baldelli, J. Mederski, A. Pomponio: Normalized solutions to Born-Infeld and quasilinear problems,
    submitted arXiv:2312.15025
  4. B. Bieganowski, A. Konysz, J. Mederski: Semiclassical states for the curl-curl problem,
    submitted arXiv:2312.03658
  5. J. Mederski, J. Schino: Normalized solutions to Schrödinger equations in the strongly sublinear regime,
    to appear in Calc. Var. Partial Differential Equations arXiv:2306.06015
  6. B. Bieganowski, J. Mederski, J. Schino: Normalized solutions to at least mass critical problems: singular polyharmonic equations and related curl-curl problems,
    submitted arXiv:2212.12361
  7. J. Mederski, W. Reichel: Travelling waves for Maxwell's equations in nonlinear and nonsymmetric media,
    NoDEA Nonlinear Differential Equations Appl. 30 (2023), no. 2, Paper No. 22, 38 pp., arXiv:2112.15146
  8. J. Mederski, A. Pomponio: Born-Infeld problem with general nonlinearity,
    J. Differential Equations 370 (2023), 470-497, arXiv:2109.10155
  9. J. Mederski, J. Schino: Nonlinear curl-curl problems in R^3,
    Minimax Theory and its Applications, 7 (2022), No. 2, 339–364 link, arXiv:2107.07396
  10. J. Mederski, J. Siemianowski: Biharmonic nonlinear scalar field equations,
    International Mathematics Research Notices 2023 (23), (2023), 19963-19995 10.1093/imrn/rnac303, arXiv:2107.07320
  11. J. Mederski, J. Schino: Least energy solutions to a cooperative system of Schrödinger equations with prescribed L^2-bounds: at least L^2-critical growth,
    Calc. Var. Partial Differential Equations 61:10 (2022), 10.1007/s00526-021-02116-0, arXiv:2101.02611
  12. P. d'Avenia, J. Mederski, A. Pomponio: Nonlinear scalar field equation with competing nonlocal terms,
    Nonlinearity 34 (2021), 5687–5707, DOI 10.1088/1361-6544/ac0d47, arXiv:2010.13184
  13. M. Gaczkowski, J. Mederski, J.Schino: Multiple solutions to cylindrically symmetric curl-curl problems and related Schrödinger equations with singular potentials,
    SIAM J. Math. Anal. 55 (2023), no. 5, 4425-4444, arXiv:2006.03565
  14. B. Bieganowski, J. Mederski: Normalized ground states of the nonlinear Schrödinger equation with at least mass critical growth,
    J. Funct. Anal. 280 (2021), no. 11, 108989 DOI 10.1016/j.jfa.2021.108989, arXiv:2002.08344
  15. J. Mederski, A. Szulkin: A Sobolev-type inequality and ground states for curl-curl problem with critical exponent,
    Arch. Rational Mech. Anal. (2021), DOI 10.1007/s00205-021-01684-x, arXiv:2002.00613
  16. B. Bieganowski, J. Mederski: Bound states for the Schrödinger equation with mixed-type nonlinearites,
    Indiana Univ. Math. J. 71 No. 1 (2022), p. 65-92 DOI 10.1512/iumj.2022.71.8662, arXiv:1905.04542
  17. 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/s00205-019-01469e3, arXiv:1901.05776
  18. J. Mederski: General class of optimal Sobolev inequalities and nonlinear scalar field equations,
    J. Differential Equations 281 (2021), 411-441 DOI 10.1016/j.jde.2021.02.015, arXiv:1812.11451
  19. 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
  20. J. Mederski: Nonradial solutions of nonlinear scalar field equations,
    Nonlinearity 33 (2020), 6349-6380, doi:10.1088/1361-6544/aba889 arXiv:1711.05711
  21. 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
  22. 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
  23. 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
  24. 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
  25. 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
  26. 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
  27. 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
  28. 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
  29. 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
  30. 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
  31. 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
  32. 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
  33. 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
  34. J. Mederski: Vietoris-Begle theorems for nonclosed maps,
    Topol. Methods Nonlinear Anal. 41 (2013), no. 1, 191-205.
  35. J. Mederski: Graph approximations of set-valued maps under constraints,
    Topol. Methods Nonlinear Anal. 39 (2012), no. 2, 361-389.
  36. J. Mederski: Equilibria of nonconvex valued maps under constraints,
    J. Math. Anal. Appl. 389 (2012), no. 2, 701-704.
  37. J. Mederski: Fiberwise absolute neighborhood extensors for a class of metrizable spaces,
    Topology Appl. 156 (2009), no. 13, 2295-2305.
  38. 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.
  39. 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:
Other: