Spectral Stability of the Neumann Laplacian

Details Spectral Stability of the Neumann Laplacian Spectral Stability of the Neumann Laplacian

2001-06-19

arxiv.org/abs/math/0106160v1

Mathematics

Spectral Theory

23 pages

Scientific paper

We prove the equivalence of Hardy- and 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 H\"older category then the eigenvalues of the Neumann Laplacian change by a small and explicitly estimated amount. AMS subject classifications: 35P15, 35J25, 47A75, 47B25, 26D10, 46E35. Keywords: Neumann Laplacian, Sobolev inequalities, Hardy inequalities, spectral stability, H\"older continuity.

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