Sobolev and Lipschitz regularity for local minimizers of widely degenerate anisotropic functionals. (April 2017)

• Record Type: Journal Article
• Authors: Brasco, Lorenzo; Leone, Chiara; Pisante, Giovanni; Verde, Anna
• Is Part Of: Nonlinear analysis. Volume 153(2017)
• Page Start: 169
• Page End: 199
• Publication Date: 2017-04
• Subjects: 35J70 -- 35B65 -- 49K20; Anisotropic problems -- Degenerate elliptic equations -- Besov–Nikol'skiĭ 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.2016.06.006
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We prove higher differentiability of bounded local minimizers to some widely degenerate functionals, verifying superquadratic anisotropic growth conditions. In the two dimensional case, we prove that local minimizers to a model functional are locally Lipschitz continuous functions, without any restriction on the anisotropy.