Glasnik matematički, Vol. 39 No. 2, 2004.
Original scientific paper
Estimates on the Dirichlet heat kernel of domains above the graphs of bounded C1,1 functions
Renming Song
Abstract
Suppose that D is the domain in , d ≥ 3, above the graph of a bounded C1,1 function : and that pD(t, x, y) is the Dirichlet heat kernel in D. In this paper we show that there exist positive constants C1, C2, C3, C4 such that for all t > 0 and x, y D,
C1((x)(y) / t 1) t -d/2 e -C|x-y|^2 / t ≤ pD(t, x, y),
pD(t, x, y) ≤ C3((x)(y) / t 1) t -d/2 e -C|x-y|^2 / t,
where (x) stands for the distance between x and D.
Keywords
Dirichlet heat kernels; Green functions; killed Brownian motions
Hrčak ID:
1250
URI
Publication date:
29.11.2004.
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