Boundary Regularity for the $\infty$-Heat Equation

Abstract

We study the boundary regularity for the normalised $\infty$-heat equation $u_t={\Delta }_{\infty }^{N}u$ in arbitrary domains. Perron's Method is used for constructing solutions. We characterize regular boundary points with barrier functions, and prove an Exterior Ball result. A Petrovsky-like criterion is established.