Some of my talks

7.09.2021 -- ‘Potential estimates for solutions to quasilinear elliptic problems with general growth. Scalar and vectorial case’, invited talk, BIRS workshop Nonlinear Potential Theoretic Methods in Partial Differential Equations, Banff, Canada (on-line) [video]

25.03.2021 -- wykład ,,Bardzo słabe rozwiązania równań różniczkowych'' na rozdaniu nagród im. Szymańskiej, Uniwersytet Adama Mickiewicza, Poznań

14.10.2020 -- wykład inauguracyjny na Wydziale Matematyki, Informatyki i Mechaniki Uniwersytetu Warszawskiego pt. ,,Zwartość kul'' (dla studentów zaczynających naukę) [prezentacja]

13.10.2020 -- talk at PolWoMath Seminar, `Local behaviour of solutions to nonstandard growth measure data problems' (for mathematicians, not necessarily analysts) [presentation]

14.06.2019 -- plenary talk during FSDONA 2019, Turku, Finland
`Density of smooth functions in Musielak-Orlicz spaces' [presentation]

Grants and awards

  • 2021, Award of III edition of Edyta Szymańska Competion, UAM Poznań
  • 2020-2025, leader of (Polish) National Science Centre Grant Sonata Bis 2019/34/E/ST1/00120 ‘Measure data problems’
  • 2019-2022, Scholarship of (Polish) Minister of Science and Higher Educations for outstanding young scientists
  • 2019, Scientific Award of >POLITYKA<
  • 2019, Honorable mention in II edition of Edyta Szymańska Competion, UAM Poznań
  • 2018, scholarship START from Foundation for Polish Science
  • 2017-2020, leader of (Polish) National Science Centre Grant Sonata 2016/23/D/ST1/01072 ‘Nonlinear differential problems in generalised Sobolev and Orlicz spaces’
  • 2017-2020, project member of (Polish) National Science Centre grant 2015/18/M/ST1/00075, leaded by Piotr Gwiazda,
  • 2015-2018, project member of (Polish) National Science Centre grant 2014/13/B/ST1/03094, leaded by Piotr Gwiazda,
  • 2012-2015, leader of (Polish) National Science Centre Grant Preludium 2011/03/N/ST1/00111 ‘Nonlinear eigenvalue problems’
  • 2010, project member of grant nr N N201 397837 funded by Polish Ministry of Science and Higher Education, leaded by Agnieszka Kałamajska
  • 2010, Special award of Ministry of Science and Higher Education in the Competition ‘Girls of Future. Following Maria Skłodowska–Curie’

Regularity of solutions in the nonstandard growth setting

I study existence and gradient estimates for elliptic problems with irregular data (merely integrable, measure, Lorentz/Morrey). The problems are posed in the Orlicz setting with not prescribed speed of growth or the fully anisotropic Orlicz setting.

Well-posedness of PDEs in the Musielak-Orlicz setting

We study existence and uniqueness of renormalized solutions to general nonlinear elliptic and parabolic equation in Musielak-Orlicz space avoiding growth restrictions. The approach does not require any particular type of growth condition of M or its conjugate M^* (neither ∆_2 , nor ∇_2). The condition we impose regularity condition on M, which can be skipped in the case of reflexive spaces. Uniqueness results from the comparison principle.

Research in collaboration with

Parabolic existence in the weighted Sobolev spaces

The research is focused on the weighted Sobolev space and its application to nonlinear parabolic problems. The framework is involved in studies on parabolic existence in the weighted setting via elliptic existence in the classical one.

Research in collaboration with

Elliptic nonexistence

The conditions sufficient to prove that solutions to certain problems are constant functions are often called nonexistence results (i.e. nonexistence of nontrivial solutions) or Liouville–type results. Growth conditions on u and - in the variable exponent case - on p(.) lead to nonexistence of entire solutions to an elliptic problem of the general form.

Research in collaboration with

Hardy-type inequalities

The objective is the new constructive method of derivation of Hardy inequalities. We derive Caccioppoli inequalities for solutions u to p-harmonic or A-harmonic problems. As a consequence we obtain weighted Hardy inequalities for compactly supported Lipschitz functions.

Research under supervision of

  • Agnieszka Kałamajska (University of Warsaw)