Multidimensional Kolmogorov-Petrovsky test for the boundary regularity and irregularity of solutions to the heat equation
© Abdulla 2005
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.