Optimal Lipschitz criteria and local estimates for non-uniformly elliptic problems

TL;DR

This paper introduces new potential theoretic techniques to establish optimal Lipschitz regularity criteria for non-uniformly elliptic variational problems, bridging the gap with uniformly elliptic cases.

Contribution

It develops a unified approach and reproduces optimal Lipschitz criteria for non-uniformly elliptic problems using novel potential theoretic methods.

Findings

Reproduces optimal Lipschitz criteria in non-uniformly elliptic setting

Introduces a new potential theoretic approach for regularity

Unifies non-uniformly and uniformly elliptic problem analysis

Abstract

We report on new techniques and results in the regularity theory of general non-uniformly elliptic variational integrals. By means of a new potential theoretic approach we reproduce, in the non-uniformly elliptic setting, the optimal criteria for Lipschitz continuity known in the uniformly elliptic one and provide a unified approach between non-uniformly and uniformly elliptic problems.