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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

Ugur G. Abdulla

Department of Mathematical Sciences, Florida Institute of Technology, Melbourne 32901, FL, USA

Received 25 August 2004

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.