Spectral Stability of the Neumann Laplacian

Abstract

We prove the equivalence of Hardyand Sobolev-type inequalities, certain uniform bounds on the heat kernel and some spectral regularity properties of the Neumann Laplacian associated with an arbitrary region of finite measure in Euclidean space. We also prove that if one perturbs the boundary of the region within a uniform Hölder category then the… (More)

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Cite this paper

@inproceedings{Burenkov2008SpectralSO, title={Spectral Stability of the Neumann Laplacian}, author={V. I. Burenkov and E. B. Davies}, year={2008} }