Gradient estimates for nonlinear elliptic double obstacle problems. (May 2020)

• Record Type: Journal Article
• Authors: Byun, Sun-Sig; Ryu, Seungjin
• Is Part Of: Nonlinear analysis. Volume 194(2020)
• Publication Date: 2020-05
• Subjects: 35J87 -- 35R05 -- 49J40; Calderón–Zygmund estimate -- Double obstacle -- Measurable nonlinearity; 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.2018.08.011
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study a nonlinear elliptic double obstacle problem with irregular data and establish an optimal Calderón–Zygmund theory. The partial differential operator is of the p -Laplacian type and includes merely measurable coefficients in one variable. We prove that the gradient of a weak solution is as integrable as both the gradient of assigned two obstacles and the nonhomogeneous divergence term under a small BMO semi-norm assumption on the coefficients in the other variables.