Remarks on the Nonlocal Dirichlet Problem
Tomasz Grzywny, Moritz Kaßmann, Łukasz Leżaj · Potential Analysis · 2020
Abstract We 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.