On Besov regularity of solutions to nonlinear elliptic partial differential equations. (March 2020)

• Record Type: Journal Article
• Authors: Dahlke, Stephan; Hansen, Markus; Schneider, Cornelia; Sickel, Winfried
• Is Part Of: Nonlinear analysis. Volume 192(2020)
• Publication Date: 2020-03
• Subjects: 41A25 -- 41A46 -- 41A65 -- 42C40 -- 65C99; (Nonlinear) elliptic equation -- Regularity of solutions -- Kondratiev spaces -- Besov spaces -- Polyhedral cones -- Domains of polyhedral type -- Linear and nonlinear approximation methods; 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.2019.111686
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we study the regularity of the solutions of some nonlinear elliptic equations in Kondratiev spaces on certain domains of polyhedral type. General embedding theorems between Kondratiev spaces and Besov spaces will allow to avoid drawbacks to the standard Sobolev regularity theory for those nonsmooth domains. This will give us the opportunity to derive optimal rates for certain nonlinear approximation schemes.