Spectral Stability of the Neumann Laplacian

2001/06/19 by V. I. Burenkov, Burenkov, V. I., E. B. Davies +1 · 1 citation
Mathematics · #26D10 #35J25 #35P15 #46E35 #47A75 #47B25 #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory (math.SP) #math.FA #math.SP #msc:26D10 #msc:35J25 #msc:35P15 #msc:46E35 #msc:47A75 #msc:47B25

paper · pdf · doi:10.48550/arxiv.math/0106160

23 pages

arxiv created 2001/06/19 · arxiv updated 2009/11/30

Abstract

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 Hölder 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, Hölder continuity.

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