Thorben Hensiek

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math.AP2023

The Dirichlet Problem for Lévy-stable operators with $L^{2}$ -data

Florian Grube, Thorben Hensiek, Waldemar Schefer

We prove Sobolev regularity for distributional solutions to the Dirichlet problem for generators of $2 s$ -stable processes and exterior data, inhomogeneity in weighted $L^{2}$ -spaces.…

math.AP2022

Maximum principle for stable operators

Florian Grube, Thorben Hensiek

We prove a weak maximum principle for nonlocal symmetric stable operators. This includes the fractional Laplacian. The main focus of this work is the regularity of the considered f…

The Dirichlet Problem for Lévy-stable operators with L2-data

Maximum principle for stable operators

The Dirichlet Problem for Lévy-stable operators with $L^{2}$ -data