Caloric functions and boundary regularity for the fractional Laplacian in Lipschitz open sets

Autor:	Armstrong, Gavin, Bogdan, Krzysztof, Rutkowski, Artur
Rok vydání:	2024
Předmět:	Mathematics - Analysis of PDEs Mathematics - Functional Analysis Mathematics - Probability 35S16 60J50 35C15
Druh dokumentu:	Working Paper
DOI:	10.1007/s00208-024-02931-8
Popis:	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 mean value property for the space-time isotropic $\alpha$-stable L\'evy process. To derive the representation, we first establish the existence of the parabolic Martin kernel. This involves proving new boundary regularity results for both the fractional heat equation and the fractional Poisson equation with Dirichlet exterior conditions. Specifically, we demonstrate that the ratio of the solution and the Green function is H\"older continuous up to the boundary. Comment: 40 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2403.03840 Zobrazit plný text záznamu View this record from Arxiv