Eigenfunctions for singular fully non linear equations in unbounded domains

TL;DR

This paper establishes Harnack inequalities for fully nonlinear degenerate elliptic equations in two dimensions and extends these results to prove the existence of eigenfunctions in smooth bounded domains.

Contribution

It extends Harnack inequalities to all dimensions for singular fully nonlinear elliptic equations and applies these to eigenfunction existence.

Findings

Harnack inequality proven for 2D degenerate elliptic equations

Extension of inequalities to all dimensions for singular cases

Existence of eigenfunctions in smooth bounded domains established

Abstract

In this paper we prove some Harnack inequality for fully non linear degenerate elliptic equations, in the two dimensional case, extending the results of Davila Felmer and Quaas in the singular case but in all dimensions. We then apply this result for the existence of an eigenfunction in smooth bounded domain.