Glasnik Matematicki, Vol. 41, No.1 (2006), 177-186.

LARGE TIME BEHAVIOR OF DIRICHLET HEAT KERNELS ON UNBOUNDED DOMAINS ABOVE THE GRAPH OF A BOUNDED LIPSCHITZ FUNCTION

Kittipat Wong

Department of Mathematics, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand
e-mail: kittipat.w@chula.ac.th

Abstract.   Let D subset 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.

2000 Mathematics Subject Classification.   60J65, 35J05.

Key words and phrases.   Dirichlet heat kernels, asymptotic behavior, Brownian motions.

Full text (PDF) (free access)

DOI: 10.3336/gm.41.1.15

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