On the strong maximum principle for fully nonlinear parabolic equations of second order

TL;DR

This paper proves strong maximum and minimum principles for fully nonlinear second-order uniformly parabolic equations using a novel parabolic approach that does not rely on the Harnack inequality.

Contribution

It introduces a new proof method for maximum principles in nonlinear parabolic equations, differing from previous approaches by Nirenberg.

Findings

Established strong maximum and minimum principles for fully nonlinear parabolic equations

Provided a proof that does not depend on the parabolic Harnack inequality

Enhanced understanding of the behavior of solutions to nonlinear parabolic PDEs

Abstract

We provide a proof of strong maximum and minimum principles for fully nonlinear uniformly parabolic equations of second order. The approach is of parabolic nature, slightly differs from the earlier one proposed by L. Nirenberg and does not exploit the parabolic Harnack inequality.