Multidimensional Kolmogorov-Petrovsky test for the boundary regularity and irregularity of solutions to the heat equation. (12th June 2005) - Abdulla, Ugur G.
Abstract : This paper establishes necessary and sufficient condition for the regularity of a characteristic top boundary point of an arbitrary open subset ofℝ N + 1 (N ≥ 2 ) for the diffusion (or heat) equation. The result implies asymptotic probability law for the standardN -dimensional Brownian motion.