Lipschitz regularity for orthotropic functionals with nonstandard growth conditions

TL;DR

This paper proves that bounded local minimizers of a convex orthotropic functional with super-quadratic nonstandard growth are locally Lipschitz, regardless of the ratio of growth rates, advancing regularity theory in this context.

Contribution

It establishes Lipschitz regularity for local minimizers of orthotropic functionals with nonstandard growth without restrictions on growth rate ratios.

Findings

Bounded local minimizers are locally Lipschitz.

No restrictions on the ratio between highest and lowest growth rates.

Advances regularity results for nonstandard growth functionals.

Abstract

We consider a model convex functional with orthotropic structure and super-quadratic nonstandard growth conditions. We prove that bounded local minimizers are locally Lipschitz, with no restrictions on the ratio between the highest and the lowest growth rate.