Heat Kernal Analysis On Weighted Dirichlet Spaces
This thesis is concerned with heat kernel estimates on weighted Dirichlet spaces. The Dirichlet forms considered here are strongly local and regular. They are defined on a complete locally compact separable metric space. The associated heat equation is similar to that of local divergence form differential operators. The weight functions studied have the form of a function of the distance from a closed set [SIGMA], that is, x [RIGHTWARDS ARROW] a(d( x, [SIGMA])). We place conditions on the geometry of the set [SIGMA] and the growth rate of function a itself. The function a can either blow up at 0 or [INFINITY] or both. Some results include the case where [SIGMA] separates the whole spaces. It can also apply to the case where [SIGMA] do not separate the space, for example, a domain Ω and its boundary [SIGMA] = ∂Ω. The condition on [SIGMA] is rather mild and do not assume differentiability condition.
poincare inequality; doubling; remotely constant
Saloff-Coste, Laurent Pascal
Cao, Xiaodong; Gross, Leonard
Ph. D., Mathematics
Doctor of Philosophy
dissertation or thesis