Remarks on the nonlocal Dirichlet problem
Analysis of PDEs
2018-07-11 v1
Abstract
We study translation-invariant integrodifferential operators that generate L\'{e}vy 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.
Cite
@article{arxiv.1807.03676,
title = {Remarks on the nonlocal Dirichlet problem},
author = {Tomasz Grzywny and Moritz Kassmann and Łukasz Leżaj},
journal= {arXiv preprint arXiv:1807.03676},
year = {2018}
}
Comments
35 pages