Local Lipschitz continuity for energy integrals with slow growth

TL;DR

This paper proves that local minimizers of certain energy integrals with slow growth are locally Lipschitz continuous, covering cases with subquadratic and anisotropic growth.

Contribution

It establishes local Lipschitz regularity for energy integrals with slow growth, including subquadratic and anisotropic cases, expanding regularity results.

Findings

Local minimizers are locally Lipschitz continuous.

Includes examples with subquadratic p,q-growth.

Addresses anisotropic growth cases.

Abstract

We consider some energy integrals under slow growth and we prove that the local minimizers are locally Lipschitz continuous. Many examples are given, either with subquadratic $p,q-$growth and/or anisotropic growth.