Spectral gap estimates for Brownian motion on domains with sticky-reflecting boundary diffusion

TL;DR

This paper develops a new interpolation method to estimate lower bounds for the spectral gap of Brownian motion on domains with sticky-reflecting boundaries, using advanced geometric analysis techniques.

Contribution

It introduces an innovative interpolation approach and applies the Reilly formula to derive spectral gap bounds for complex boundary conditions.

Findings

Derived lower bounds for spectral gaps in general domains

Applied Reilly formula in novel ways for boundary diffusion

Extended spectral analysis to sticky-reflecting boundary conditions

Abstract

Introducing an interpolation method we derive lower bounds for the spectral gap for Brownian motion on general domains with sticky-reflecting boundary diffusion associated to the first nontrivial eigenvalue for the Laplace operator with corresponding Wentzell-type boundary condition. In the manifold case our proofs involve novel applications of the celebrated Reilly formula.