# Regularity for solutions of fully nonlinear elliptic equations with non-homogeneous degeneracy

## TL;DR

This paper proves that viscosity solutions to certain fully nonlinear elliptic equations with double phase degeneracy are locally $C^{1,eta}$ regular, advancing understanding of their smoothness properties.

## Contribution

It establishes local $C^{1,eta}$ regularity for solutions of fully nonlinear elliptic equations with double phase degeneracy, a novel regularity result for this class of equations.

## Key findings

- Viscosity solutions are locally $C^{1,eta}$ regular.
- Regularity holds despite degeneracy of double phase type.
- Advances understanding of solution smoothness in degenerate elliptic equations.

## Abstract

We prove that viscosity solutions to fully nonlinear elliptic equations with degeneracy of double phase type are locally $C^{1,\gamma}$-regular.