4 citations · 6 across the 7 of their papers we have counts for
9 papers
Singular semilinear elliptic equations in nondivergence form
Agnieszka Kałamajska, Dalimil Peša, Artur Rutkowski
We study the singular semilinear equation on a bounded domain with Dirichlet condition on , where is a second-order elliptic…
Caloric functions and boundary regularity for the fractional Laplacian in Lipschitz open sets
Gavin Armstrong, Krzysztof Bogdan, Artur Rutkowski
We give Martin representation of nonnegative functions caloric with respect to the fractional Laplacian in Lipschitz open sets. The caloric functions are defined in terms of the me…
The master equation for mean field game systems with fractional and nonlocal diffusions
Espen Robstad Jakobsen, Artur Rutkowski
We prove existence and uniqueness of classical solutions of the master equation for mean field game (MFG) systems with fractional and nonlocal diffusions. We cover a large class of…
The Douglas formula in
Krzysztof Bogdan, Damian Fafuła, Artur Rutkowski
We prove a Douglas-type identity in for .
Fractional Korn's inequality on subsets of the Euclidean space
Artur Rutkowski
We give a new, simpler proof of the fractional Korn's inequality for subsets of . We also show a framework for obtaining Korn's inequality directly from the appropria…
Nonlinear nonlocal Douglas identity
Krzysztof Bogdan, Tomasz Grzywny, Katarzyna Pietruska-Pałuba +1
We give Hardy-Stein and Douglas identities for nonlinear nonlocal Sobolev-Bregman integral forms with unimodal Lévy measures. We prove that the corresponding Poisson integral defin…
Reduction of integration domain in Triebel-Lizorkin spaces
Artur Rutkowski
We investigate the comparability of generalized Triebel--Lizorkin and Sobolev seminorms on uniform and non-uniform sets when the integration domain is truncated according to the di…
Extension and trace for nonlocal operators
Krzysztof Bogdan, Tomasz Grzywny, Katarzyna Pietruska-Pałuba +1
We prove an optimal extension and trace theorem for Sobolev spaces of nonlocal operators. The extension is given by a suitable Poisson integral and solves the corresponding nonloca…
The Dirichlet problem for nonlocal Lévy-type operators
Artur Rutkowski
We present the theory of the Dirichlet problem for nonlocal operators which are the generators of general pure-jump symmetric Lévy processes whose Lévy measures need not be absolut…