$www.math.cornell.edu$

Pavel Gyrya

Augut 2007 Ph.D.

First Position

Risk manager for American Express

Dissertation

Heat Kernel Estimates for Inner Uniform Subsets of Harnack-Type Dirichlet Spaces

Advisor:

Laurent Saloff-Coste

Research Area:

partial differential equations

Abstract: The main result of this thesis is the two-sided heat kernel estimates for both Dirichlet and Neumann problem in a inner uniform domain of Rⁿ, and many other spaces with Gaussian-type heat kernel estimates. We assume that the heat equation is associated with a local divergence form differential operator, or more generally with a strictly local Dirichlet form on a complete locally compact metric space. Other results include the (parabolic) Harnack inequality and the boundary Harnack principle.