A Microscopic Convexity Principle for Nonlinear Partial Differential Equations

TL;DR

This paper introduces a microscopic convexity principle applicable to nonlinear elliptic and parabolic PDEs, providing a new theoretical framework for analyzing their solutions.

Contribution

It presents a novel microscopic convexity principle that broadens the understanding of nonlinear PDEs in a general form.

Findings

Established a convexity principle for nonlinear PDEs

Applicable to elliptic and parabolic equations

Provides new insights into solution properties

Abstract

We establish a microscopic convexity principle for nonlinear elliptic and parabolic partial differential equations in general form.