Nonlinear gradient estimates for generalized elliptic equations with nonstandard growth in nonsmooth domains. (July 2016)

• Record Type: Journal Article
• Authors: Byun, Sun-Sig; Cho, Yumi
• Is Part Of: Nonlinear analysis. Volume 140(2016)
• Page Start: 145
• Page End: 165
• Publication Date: 2016-07
• Subjects: primary 35J60 35B65 -- secondary 46E30 46E35; Nonlinear gradient estimate -- Elliptic equation -- Nonstandard growth -- Orlicz space -- 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.2016.03.016
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: A generalized elliptic equation with nonstandard growth in a nonsmooth bounded domain is studied. A global nonlinear gradient estimate is obtained in the frame of Orlicz spaces under the assumptions that the associated Young functions satisfy some moderate growth and decay conditions and that the boundary of the domain is δ -Reifenberg flat with δ depending on the domain, the dimension of the domain and the Young functions.