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
 Assistant Professor (on leave) at Nicolaus Copernicus University
  MathSciNet Google Scholar
[Home] [Research interests] [Short CV [SONATA BIS project] [Publications] [Teaching] [Other]

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:

A new PhD position is available.

The successfull candidate will obtain the state PhD Scholarship as well as the scholarship of the NCN grant. If you have any questions, please don't hesitate to contact me jmederski at impan dot pl . Deadline is in June 2020, but feel free to contact me earlier.

Publications:
  1. B. Bieganowski, J. Mederski: Normalized ground states of the nonlinear Schrödinger equation with at least mass critical growth,
    submitted arXiv:2002.08344
  2. J. Mederski, A. Szulkin: Sharp constant in the curl inequality and ground states for curl-curl problem with critical exponent,
    submitted arXiv:2002.00613
  3. B. Bieganowski, J. Mederski: Bound states for the Schrödinger equation with mixed-type nonlinearites,
    submitted arXiv:1905.04542
  4. J. Mederski, J. Schino, A. Szulkin: Multiple solutions to a nonlinear curl-curl problem in R^3,
    to appear in Archive for Rational Mechanics and Analysis DOI 10.1007/s00205-019-01469-3 arXiv:1901.05776
  5. J. Mederski: General class of optimal Sobolev inequalities and nonlinear scalar field equations,
    submitted arXiv:1812.11451
  6. 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
  7. J. Mederski: Nonradial solutions of nonlinear scalar field equations,
    submitted arXiv:1711.05711
  8. 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
  9. 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
  10. 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
  11. 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
  12. 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
  13. 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
  14. 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
  15. 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
  16. 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
  17. 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
  18. 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
  19. 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
  20. 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
  21. J. Mederski: Vietoris-Begle theorems for nonclosed maps,
    Topol. Methods Nonlinear Anal. 41 (2013), no. 1, 191-205.
  22. J. Mederski: Graph approximations of set-valued maps under constraints,
    Topol. Methods Nonlinear Anal. 39 (2012), no. 2, 361-389.
  23. J. Mederski: Equilibria of nonconvex valued maps under constraints,
    J. Math. Anal. Appl. 389 (2012), no. 2, 701-704.
  24. J. Mederski: Fiberwise absolute neighborhood extensors for a class of metrizable spaces,
    Topology Appl. 156 (2009), no. 13, 2295-2305.
  25. 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.
  26. 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, financial and actuarial mathematics, SQL and databases - Oracle, C++ programming. Teaching materials (in Polish):

Other: