Large Time Behavior of Dirichlet Heat Kernels on Unbounded Domains above the Graph of a Bounded Lipschitz Function

Abstract

Let D ⊆ Rd, d ≥ 2 be the unbounded domain above the graph of a bounded Lipschitz function. We study the asymptotic behavior of the transition density pD(t, x, y) of killed Brownian motions in D and show that limt→∞ t d+2 2 pD(t, x, y) = C1u(x)u(y), where u is a minimal harmonic function corresponding to the Martin point at infinity and C1 is a positive… (More)

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Cite this paper

@inproceedings{WongLargeTB, title={Large Time Behavior of Dirichlet Heat Kernels on Unbounded Domains above the Graph of a Bounded Lipschitz Function}, author={Kittipat Wong and K. Wong} }