Heat Kernel estimates for general boundary problems

Abstract

We show that not feeling the boundary estimates for heat kernels hold for any non-negative self-adjoint extension of the Laplace operator acting on vector-valued compactly supported functions on a domain in ${\mathbb{R}}^d$. They are therefore valid for any choice of boundary condition and we show that the implied constants can be chosen independent of the self-adjoint extension. The method of proof is very general and is based on finite propagation speed estimates and explicit Fourier Tauberian theorems obtained by Y. Safarov.

13 pages, latex

References in corpus (1)

• Gaussian heat kernel upper bounds via Phragmén-Lindelöf theorem