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Lipschitz Regularity of Minimizers of Variational Integrals with Variable Exponents by Eleuteri, Michela; di Napoli, Antonia Passarelli is a scholarly article available to read on EtoBox.

What is Lipschitz Regularity of Minimizers of Variational Integrals with Variable Exponents about?

In this paper we prove the Lipschitz regularity for local minimizers of convex variational integrals of the form \[ \mathfrak{F}( v, \Omega )= \int_{\Omega} \! F(x, Dv(x)) \, dx, \] where, for ${n > 2}$ and $N\ge 1$, $\Omega$ is a bounded open set in $\mathbb{R}^n$, $u \in W^{1,1}(\Omega , \mathbb{R}^N)$ and the energy density $F:\Omega\times \mathbb{R}^{N \times n}\to \mathbb{R}$ satisfies the so called variable growth conditions. The main novelty of the paper is that we assume an almost critical regularity in the Orlicz Sobolev setting for the energy density as a function of the $x$ variable.

Author

Eleuteri, Michela; di Napoli, Antonia Passarelli

Published

2022

Language

EN