Remarks on the Nonlocal Dirichlet Problem

Author:

Grzywny Tomasz,Kassmann Moritz,Leżaj Łukasz

Abstract

AbstractWe study translation-invariant integrodifferential operators that generate Lévy processes. First, we investigate different notions of what a solution to a nonlocal Dirichlet problem is and we provide the classical representation formula for distributional solutions. Second, we study the question under which assumptions distributional solutions are twice differentiable in the classical sense. Sufficient conditions and counterexamples are provided.

Publisher

Springer Science and Business Media LLC

Subject

Analysis

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