On the level set version of partial uniform ellipticity and applications

TL;DR

This paper introduces a level set approach to partial uniform ellipticity for symmetric concave functions, providing a new method to analyze second order fully nonlinear elliptic and parabolic equations.

Contribution

It develops a level set framework for partial uniform ellipticity, offering a novel tool for studying complex nonlinear PDEs.

Findings

New level set formulation for partial uniform ellipticity

Effective approach for second order fully nonlinear equations

Potential applications to elliptic and parabolic PDEs

Abstract

We derive level set version of partial uniform ellipticity for symmetric concave functions. This suggests an effective approach to investigate second order fully nonlinear equations of elliptic and parabolic type.