The Boundary Behavior of Heat Kernels of Dirichlet Laplacians

We prove the following complete and qualitatively sharp description of heat kernels G of Dirichlet Laplacians on bounded C1,1 domains D. There exist positive constants c1,c2 and T>0 depending on D such that, for ρ(x)=dist(x,∂D), for all x,y D and 0T are known.) Bounds when D is unbounded are also given.