Abstract
After a short survey of some of the reasons that make the heat kernel an important object of study, we review a number of basic heat kernel estimates. We then describe recent results concerning (a) the heat kernel on certain manifolds with ends, and (b) the heat kernel with the Neumann or Dirichlet boundary condition in inner uniform Euclidean domains.
Information
Published: 1 January 2010
First available in Project Euclid: 24 November 2018
zbMATH: 1201.58025
MathSciNet: MR2648271
Digital Object Identifier: 10.2969/aspm/05710405
Subjects:
Primary:
35K05
,
58J65
,
60J65
Keywords:
Brownian motion
,
heat kernel
,
uniform domains
Rights: Copyright © 2010 Mathematical Society of Japan
