Accepted Paper

Inserted: 17 oct 2012
Last Updated: 22 oct 2012

Journal: Advances in Calculus of Variations
Year: 2012

Abstract:

In this paper we consider integral functionals with convex integrand satisfying p growth conditions with respect to the gradient variable. As a novel feature, the dependence of the integrand on the x-variable is allowed to be through a Sobolev function. We prove local higher differentiability results for local minimizers of the functional F, establishing uniform higher differentiability estimates for solutions to a class of auxiliary problems, constructed adding singular higher order perturbations to the integrand. Furthermore, we prove a dimension free higher integrability result for the gradient of local minimizers, by the use of a weighted version of the Gagliardo-Nirenberg interpolation inequality.

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• sobolevcoeffrev2.pdf