Boundary pointwise regularity and Liouville theorems for fully nonlinear equations on cones

TL;DR

This paper establishes boundary pointwise regularity for fully nonlinear elliptic equations on cones and uses this to provide simplified proofs of Liouville theorems in the same setting.

Contribution

It introduces new boundary regularity results for fully nonlinear equations on cones and leverages these to simplify proofs of Liouville theorems.

Findings

Boundary pointwise regularity for fully nonlinear elliptic equations on cones

Simplified proofs of Liouville theorems on cones

Enhanced understanding of elliptic equations in conical domains

Abstract

In this paper, we prove a boundary pointwise regularity for fully nonlinear elliptic equations on cones. In addition, based on this regularity, we give simple proofs of the Liouville theorems on cones.