Heat Kernel estimates for general boundary problems

2016/04/04 by Li, Liangpan, Strohmaier, Alexander · 1 citation
#35K08 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1604.00784

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 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.

Cited by

• Fluctuations for the critical free Bose gas

Related

• Pointwise Lower bounds on the Heat Kernels of Uniformally Elliptic Operators in Bounded Regions
• On gradient estimates for the heat kernel
• Functional calculus of operators with heat kernel bounds on non-doubling manifolds with ends
• Square function and heat flow estimates on domains
• L^p estimate of the heat equation on a bounded domain