Large time behavior of Dirichlet heat kernels on unbounded domains above the graph of a bounded Lipschitz function
Kittipat Wong · Glasnik Matematicki · 2006
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!1 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 innity and C1 is a positive constant. 1.