Estimates on the Dirichlet heat kernel of domains above the graphs of bounded C1,1 functions
Renming Song · Glasnik Matematicki · 2004
Suppose that D is the domain in R d , d ≥ 3, above the graph of a bounded C 1,1 function Γ : R d-1 → R and that p D (t, x, y) is the Dirichlet heat kernel in D. In this paper we show that there exist positive constants C 1 , C 2 , C 3 and C 4 such that for all t > 0 and x, y ∈ D,where ρ(x) stands for the distance between x and ∂D.