Heat kernel estimates for inner uniform subsets of Harnack-type Dirichlet space
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The main result of this thesis is the two-sided heat kernel
estimates for both Dirichlet and Neumann problem in any inner
uniform domain of the Euclidean space $\mathbb R^n$. The results
of this thesis hold more generally for any inner uniform domain in
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.
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2007-06-19T19:57:32Z
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heat kernel estimates; Harnack; inner uniform set; Dirichlet form
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Government Document
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dissertation or thesis