Artur Rutkowski

activity

20182026

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math.AP2026

Singular semilinear elliptic equations in nondivergence form

Agnieszka Kałamajska, Dalimil Peša, Artur Rutkowski

We study the singular semilinear equation $- P u = \frac{f}{u ^{γ}}$ on a bounded domain $Ω$ with Dirichlet condition $u \equiv 0$ on $\partial Ω$ , where $P$ is a second-order elliptic…

math.AP2024

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…