Regularity of flat free boundaries for a p(x)-Laplacian problem with right hand side. (November 2021)

• Record Type: Journal Article
• Authors: Ferrari, Fausto; Lederman, Claudia
• Is Part Of: Nonlinear analysis. Volume 212(2021)
• Publication Date: 2021-11
• Subjects: 35R35 -- 35B65 -- 35J60 -- 35J70; Free boundary problem -- Singular/degenerate operator -- Variable exponent spaces -- Regularity of the free boundary -- Non-zero right hand side -- Viscosity solutions; 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.2021.112444
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider viscosity solutions to a one-phase free boundary problem for the p ( x ) -Laplacian with non-zero right hand side. We apply the tools developed in De Silva (2011) to prove that flat free boundaries are C 1, α . Moreover, we obtain some new results for the operator under consideration that are of independent interest.