The Dirichlet problem for nonlocal Lévy-type operators

2017/02/03 by Artur Rutkowski, Rutkowski, Artur
Mathematics · #35S15 #47G20 #60G51 #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1702.01054

openalex publication_date 2017/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present the theory of the Dirichlet problem for nonlocal operators which are the generators of general pure-jump symmetric Lévy processes whose Lévy measures need not be absolutely continuous. We establish basic facts about the Sobolev spaces for such operators, in particular we prove the existence and uniqueness of weak solutions. We present strong and weak variants of maximum principle, and L^∞ bounds for solutions. We also discuss the related extension problem in C^1,1 domains.

Citations

• Function spaces and extension results for nonlocal Dirichlet problems

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