Accepted Paper

Inserted: 31 jul 2026
Last Updated: 31 jul 2026

Journal: Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni
Volume: 27
Number: (1)
Pages: 61-87
Year: 2016
Doi: 10.4171/RLM/723

Abstract:

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 $W^{1,r}_{\rm loc}(\Omega)$ for some $r > n$, is locally Lipschitz continuous in $\Omega$ and an a priori estimate holds.

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