Hs, p regularity theory for a class of nonlocal elliptic equations. (June 2020)

• Record Type: Journal Article
• Authors: Nowak, Simon
• Is Part Of: Nonlinear analysis. Volume 195(2020)
• Publication Date: 2020-06
• Subjects: 35R09 -- 35B65 -- 35D30 -- 46E35 -- 47G20; Nonlocal operators -- Elliptic equations -- Regularity theory -- Bessel potential spaces; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.111730
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we study the regularity of weak solutions to a class of nonlocal elliptic equations in Bessel potential spaces H s, p . Our main results can be seen as an extension of the well-known W 1, p regularity theory for local second-order elliptic equations in divergence form to the nonlocal setting.