Generalizations of Stampacchia Lemma and applications to quasilinear elliptic systems. (July 2021)

• Record Type: Journal Article
• Authors: Gao, Hongya; Deng, Hua; Huang, Miaomiao; Ren, Wei
• Is Part Of: Nonlinear analysis. Volume 208(2021)
• Publication Date: 2021-07
• Subjects: 35J57; Stampacchia Lemma -- Quasilinear elliptic system -- Ellipticity -- Degenerate ellipticity -- Global regularity; 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.2021.112297
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We present two generalizations of the classical Stampacchia Lemma. As applications, we consider Dirichlet problem for elliptic systems of the form − ∑ i = 1 n ∂ ∂ x i ∑ β = 1 N ∑ j = 1 n a i, j α, β ( x, u ( x ) ) ∂ u β ( x ) ∂ x j = f α, in Ω, u ( x ) = 0, on ∂ Ω . Under ellipticity and degenerate ellipticity conditions of the diagonal coefficients and proportional conditions of the off-diagonal coefficients, we derive some global regularity results.