Removable Singularities of $m$-Hessian Equations

TL;DR

This paper introduces a less restrictive condition for the removability of singularities in solutions to m-Hessian and similar fully nonlinear elliptic equations, relying on classical elliptic theory tools.

Contribution

It provides a new criterion for singularity removability that simplifies previous conditions and applies to a broad class of fully nonlinear elliptic equations.

Findings

New less restrictive condition for singularity removability

Applicability to m-Hessian and general fully nonlinear elliptic equations

Proofs based solely on classical elliptic theory tools

Abstract

In this paper we give a new, less restrictive condition for removability of singular sets, $E$, of smooth solutions to the m-Hessian equation (and also for more general fully nonlinear elliptic equations) in $\Omega \setminus E$, $\Omega \subset \mathbb R^n$. Besides the existence and regularity results for these equations, the proof only makes use of the classical elliptic theory, i.e. the classical maximum principles and a Hopf lemma.