Lipschitz regularity for anisotropic fully nonlinear equations with nonstandard growth

TL;DR

This paper proves interior Lipschitz regularity for solutions to anisotropic fully nonlinear equations with nonstandard growth, extending existing theories without restrictions on growth exponent gaps, using an anisotropic Ishii Lions method.

Contribution

It introduces an anisotropic approach to establish Lipschitz regularity for complex nonlinear equations with nonstandard growth, without growth gap restrictions.

Findings

Established interior Lipschitz regularity for solutions

Extended the viscosity analogue of divergence-form theory

Applied anisotropic Ishii Lions method successfully

Abstract

We establish interior Lipschitz regularity for solutions to anisotropic fully nonlinear equations with nonstandard growth, without imposing any restriction on the gap between the highest and lowest growth exponents. Our proof is based on an anisotropic variant of the seminal Ishii Lions method. Our result furnishes a viscosity analogue of the divergence-form theory in [Bousquet20], adapted to the non-divergence setting.