Remarks on the nonlocal Dirichlet problem
Abstract
We study translation-invariant integrodifferential operators that generate L\'evy 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.
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