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]
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.
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
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
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
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