Boundary behavior of nonnegative solutions of fully nonlinear parabolic equations

TL;DR

This paper investigates how nonnegative solutions to fully nonlinear parabolic equations behave near boundaries, establishing comparison principles and inequalities that enhance understanding of their boundary regularity.

Contribution

It provides new comparison theorems and a backward Harnack inequality for viscosity solutions of fully nonlinear parabolic equations.

Findings

Established local and global comparison theorems in $C^{1,1}$ cylinders.

Proved a backward Harnack inequality for solutions.

Enhanced understanding of boundary behavior of nonlinear parabolic equations.

Abstract

We study the boundary behavior of viscosity nonnegative solutions of fully nonlinear parabolic Pucci extremal operators. We establish local and global comparison theorems in $C^{1,1} cylinders, along with a backward Harnack inequality.