A boundary regularity result for minimizers of variational integrals with nonstandard growth. (December 2018)

• Record Type: Journal Article
• Authors: Bulíček, Miroslav; Maringová, Erika; Stroffolini, Bianca; Verde, Anna
• Is Part Of: Nonlinear analysis. Volume 177(2018)Part A
• Page Start: 153
• Page End: 168
• Publication Date: 2018-12
• Subjects: 35J47 -- 35J25; Elliptic system -- Existence of solutions -- Nonstandard growth conditions -- Boundary 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.2018.03.001
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We prove global Lipschitz regularity for a wide class of convex variational integrals among all functions in W 1, 1 with prescribed (sufficiently regular) boundary values, which are not assumed to satisfy any geometrical constraint (as for example bounded slope condition). Furthermore, we do not assume any restrictive assumption on the geometry of the domain and the result is valid for all sufficiently smooth domains. The result is achieved with a suitable approximation of the functional together with a new construction of appropriate barrier functions.