Global L∞-estimates and Hölder continuity of weak solutions to elliptic equations with the general nonstandard growth conditions. (June 2017)

• Record Type: Journal Article
• Authors: Yu, Cholhun; Ri, Dukman
• Is Part Of: Nonlinear analysis. Volume 156(2017)
• Page Start: 144
• Page End: 166
• Publication Date: 2017-06
• Subjects: 35B65 -- 35D30 -- 76A05; Nonstandard growth -- L∞-estimate -- Hölder continuity -- Variable exponent; 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.2017.02.019
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study the elliptic equations in divergence form with the general nonstandard growth conditions involving Lebesgue measurable functions on Ω . In this paper we prove global L ∞ -estimates and Hölder continuity of weak solutions for these equations. Our results improve the one in Giusti (2003) even for the case when p ( x ) ≡ p and q ( x ) ≡ q are constants.