ABP and global Holder estimates for fully nonlinear elliptic equations in unbounded domains

TL;DR

This paper establishes global Hölder continuity estimates for solutions to fully nonlinear elliptic and degenerate elliptic equations in unbounded domains, under specific geometric conditions on the domain.

Contribution

It provides the first global Hölder estimates for such equations in unbounded domains with geometric conditions similar to Cabre's.

Findings

Proved global Hölder estimates for solutions.

Applicable to fully nonlinear and degenerate elliptic equations.

Works in unbounded domains with geometric conditions.

Abstract

We prove global Holder estimates for solution of fully nonlinear elliptic or degenerate elliptic equations in unbounded domains under geometric conditions on the domain a' la Cabre'.