Interior regularity estimates for fully nonlinear equations with arbitrary nonhomogeneous degeneracy laws

TL;DR

This paper develops interior regularity estimates for a broad class of degenerate, fully nonlinear elliptic equations with nonhomogeneous degeneracy, showing solutions are locally continuously differentiable.

Contribution

It introduces a novel recursive renormalization algorithm and extends regularity results to equations with arbitrary nonhomogeneous degeneracy laws.

Findings

Viscosity solutions are locally continuously differentiable.

Improvement of flatness technique is effectively applied.

New recursive algorithm links degenerate equations to uniform elliptic ones.

Abstract

In this paper, we study regularity estimates for a class of degenerate, fully nonlinear elliptic equations with arbitrary nonhomogeneous degeneracy laws. We establish that viscosity solutions are locally continuously differentiable under suitable conditions on the degeneracy laws. Our proof employs improvement of flatness techniques alongside an alternative recursive algorithm for renormalizing the approximating solutions, linking our model to the homogeneous, fully nonlinear, uniformly elliptic equation.