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
Department of Mathematical Sciences, Florida Institute of Technology, Melbourne 32901, FL, USA
Received 25 August 2004
Copyright © 2005 Ugur G. Abdulla. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.