English

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.

Keywords

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

R2 v1 2026-06-23T02:56:27.977Z