Glasnik matematički, Vol. 41 No. 1, 2006.
Original scientific paper
Large time behavior of Dirichlet heat kernels on unbounded domains above the graph of a bounded Lipschitz function
Kittipat Wong
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 constant.
Keywords
Dirichlet heat kernels; asymptotic behavior; Brownian motions
Hrčak ID:
3308
URI
Publication date:
24.5.2006.
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