Higher integrability for minimizers of asymptotically convex integrals with discontinuous coefficients. (May 2017)

• Record Type: Journal Article
• Authors: Cupini, Giovanni; Giannetti, Flavia; Giova, Raffaella; Passarelli di Napoli, Antonia
• Is Part Of: Nonlinear analysis. Volume 154(2017)
• Page Start: 7
• Page End: 24
• Publication Date: 2017-05
• Subjects: primary 49N60 49N99 -- secondary 35J47; Regularity of minimizers -- Asymptotic convexity -- p-growth; 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.2016.02.017
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study the local regularity of vectorial minimizers of integral functionals with standard p -growth. We assume that the non-homogeneous densities are uniformly convex and have a radial structure, with respect to the gradient variable, only at infinity. Under a W 1, n -Sobolev dependence on the spatial variable of the integrand, n being the space dimension, we show that the minimizers have the gradient locally in L q for every q > p . As a consequence, they are locally α -Hölder continuous for every α < 1 .