Boundary regularity for a general nonlinear parabolic equation in non-divergence form

TL;DR

This paper characterizes boundary point regularity for a broad class of nonlinear parabolic equations, providing geometric conditions for regularity and highlighting limitations when q<2.

Contribution

It introduces a barrier family characterization for boundary regularity in general nonlinear parabolic equations, extending previous results to more complex equations.

Findings

Boundary regularity characterized via barrier families.

Geometric conditions established for regularity.

Single barrier insufficient for q<2.

Abstract

We characterize regular boundary points in terms of a barrier family for a general form of a parabolic equation that generalizes both the standard parabolic $p$-Laplace equation and the normalized version arising from stochastic game theory. Using this result we prove geometric conditions that ensure regularity by constructing suitable barrier families. We also prove that when $q<2$, a single barrier does not suffice to guarantee regularity.