Higher differentiability of minimizers of convex variational integrals

Author: 

Carozza, M
Kristensen, J
Passarelli Di Napoli, A

Publication Date: 

1 January 2011

Journal: 

Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

Last Updated: 

2019-04-23T23:59:35.737+01:00

Issue: 

3

Volume: 

28

DOI: 

10.1016/j.anihpc.2011.02.005

page: 

395-411

abstract: 

In this paper we consider integral functionals of the formF(v,Ω)= ∫ΩF(Dv(x))dx with convex integrand satisfying (p,q) growth conditions. We prove local higher differentiability results for bounded minimizers of the functional F under dimension-free conditions on the gap between the growth and the coercivity exponents. As a novel feature, the main results are achieved through uniform higher differentiability estimates for solutions to a class of auxiliary problems, constructed adding singular higher order perturbations to the integrand. © 2011 Elsevier Masson SAS. All rights reserved.

Symplectic id: 

149814

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article