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  • Research Article
  • 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:


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, Melbourne, FL 32901, USA


© Abdulla 2005