Lipschitz regularity for degenerate elliptic integrals with p,q-growth

TL;DR

This paper proves local Lipschitz continuity and higher differentiability of minimizers for a class of degenerate elliptic integrals with p,q-growth, addressing challenges due to degeneracy in the energy densities.

Contribution

It introduces new regularity results for vector-valued minimizers of degenerate energy integrals with p,q-growth, handling degeneracy in the x-variable.

Findings

Established local Lipschitz continuity of minimizers

Proved higher differentiability of minimizers

Addressed degeneracy in energy densities with respect to x-variable

Abstract

We establish the local Lipschitz continuity and the higher differentiability of vector-valued local minimizers of a class of energy integrals of the Calculus of Variations. The main novelty is that we deal with possibly degenerate energy densities with respect to the x-variable.