Boundary Value Problems
Volume 2005 (2005), Issue 2, Pages 181-199
doi:10.1155/BVP.2005.181

Multidimensional Kolmogorov-Petrovsky test for the boundary regularity and irregularity of solutions to the heat equation

Abstract

This paper establishes necessary and sufficient condition for the regularity of a characteristic top boundary point of an arbitrary open subset of ℝN+1 (N≥2) for the diffusion (or heat) equation. The result implies asymptotic probability law for the standard N-dimensional Brownian motion.