Gradient regularity for quasilinear elliptic Dirichlet problems in the plane. (November 2016)

• Record Type: Journal Article
• Authors: Alberico, Angela; Cianchi, Andrea; Sbordone, Carlo
• Is Part Of: Nonlinear analysis. Volume 145(2016)
• Page Start: 143
• Page End: 161
• Publication Date: 2016-11
• Subjects: 35B65 -- 35J60 -- 46E30; Quasilinear elliptic equations -- Measurable coefficients -- Gradient regularity -- Rearrangement-invariant spaces -- Orlicz spaces; 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.2016.08.005
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The problem is addressed of the maximal integrability of the gradient of solutions to quasilinear elliptic equations, with merely measurable coefficients, in two variables. Optimal results are obtained in the framework of Orlicz spaces, and in the more general setting of all rearrangement-invariant spaces. Applications to special instances are exhibited, which provide new gradient bounds, or improve certain results available in the literature.