Gradient estimates for p-Laplacian equation in composite Reifenberg domains. (March 2016)

• Record Type: Journal Article
• Authors: Zhang, Chao
• Is Part Of: Nonlinear analysis. Volume 133(2016)
• Page Start: 134
• Page End: 143
• Publication Date: 2016-03
• Subjects: primary 35R05 35R35 -- secondary 35J15 35J25; Elliptic -- p-Laplacian -- Gradient estimate -- Composite Reifenberg domain; 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.2015.11.028
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We obtain a local gradient estimate for weak solutions of p -Laplacian type equation in a non-smooth domain composed of a finite number of disjoint subdomains with ( δ 0, R ) -Reifenberg flat boundaries. This kind of domain was called ( δ 0, R ) composite-Reifenberg domain, which allows certain subdomain to exist with highly non-smooth boundaries worse than Reifenberg domain. Our results improve the known results for such equations.