Open Access

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

Boundary Value Problems20052005:289712

Received: 25 August 2004

Published: 12 June 2005


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

Authors’ Affiliations

Department of Mathematical Sciences, Florida Institute of Technology


© Abdulla 2005