Rendiconti Lincei - Matematica e Applicazioni


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Volume 27, Issue 1, 2016, pp. 61–87
DOI: 10.4171/RLM/723

Published online: 2016-02-29

Lipschitz continuity for energy integrals with variable exponents

Michela Eleuteri[1], Paolo Marcellini[2] and Elvira Mascolo[3]

(1) Università di Firenze, Italy
(2) Università di Firenze, Italy
(3) Università di Firenze, Italy

A regularity result for integrals of the Calculus of Variations with variable exponents is presented. Precisely, we prove that any vector-valued minimizer of an energy integral over an open set $\Omega \subset \mathbb R^n$, with variable exponent $p(x)$ in the Sobolev class $W^{1,r}_\mathrm {loc} (\Omega)$ for some $r > n$, is locally Lipschitz continuous in $\Omega$ and an a priori estimate holds.

Keywords: Energy integrals, local minimizers, local Lipschitz continuity, $p(x)$-growth, variable exponents

Eleuteri Michela, Marcellini Paolo, Mascolo Elvira: Lipschitz continuity for energy integrals with variable exponents. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 27 (2016), 61-87. doi: 10.4171/RLM/723