Schroedinger operators on exterior domains with Robin boundary conditions: heat kernel estimates

TL;DR

This paper investigates Schrödinger operators with Robin boundary conditions on exterior domains, providing sharp heat kernel estimates that reveal how boundary conditions influence heat decay, with implications for spectral analysis.

Contribution

It offers new sharp point-wise heat kernel estimates for Schrödinger operators with Robin boundary conditions on exterior domains, highlighting boundary effects on heat decay.

Findings

Boundary conditions significantly affect heat kernel decay rates.

Sharp point-wise estimates are established for dimensions one and two.

Applications to spectral estimates are demonstrated.

Abstract

We study Schroedinger operators with Robin boundary conditions on exterior domains in $\R^d$. We prove sharp point-wise estimates for the associated semi-groups which show, in particular, how the boundary conditions affect the time decay of the heat kernel in dimensions one and two. Applications to spectral estimates are discussed as well.