A regularity result for a class of non-uniformly elliptic operators

TL;DR

This paper establishes an explicit Hölder regularity result for viscosity solutions of certain fully nonlinear second-order equations that are neither convex nor uniformly elliptic, expanding understanding of solution regularity in complex PDEs.

Contribution

It provides a new regularity result for a class of non-uniformly elliptic operators, which are neither convex nor concave, filling a gap in PDE regularity theory.

Findings

Viscosity solutions are Hölder continuous under specified conditions.

The regularity result applies to a broader class of operators than previously known.

Explicit estimates for the Hölder continuity are derived.

Abstract

We obtain an explicit H\"older regularity result for viscosity solutions of a class of second order fully nonlinear equations leaded by operator that are neither convex/concave nor uniformly elliptic.