Regularity estimates for nonlinear elliptic measure data problems with nonstandard growth. (May 2019)

• Record Type: Journal Article
• Authors: Byun, Sun-Sig; Liang, Shuang; Youn, Yeonghun
• Is Part Of: Nonlinear analysis. Volume 182(2019)
• Page Start: 303
• Page End: 315
• Publication Date: 2019-05
• Subjects: 35R06 -- 35B65; Measure data -- Calderón–Zygmund estimate -- Nonstandard growth; 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.2019.01.002
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We prove a global Calderón–Zygmund type estimate for the gradient of a solution to a nonlinear elliptic problem with nonstandard growth when the right-hand side is a bounded Radon measure. Minimal regularity requirements on both the nonlinearity and the boundary of the domain are investigated for such a gradient estimate.