Spectral Asymptotics for Dirichlet to Neumann Operator in the Domains with Edges

Victor Ivrii ()
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Victor Ivrii: University of Toronto, Department of Mathematics

Chapter Chapter 31 in Microlocal Analysis, Sharp Spectral Asymptotics and Applications V, 2019, pp 513-539 from Springer

Abstract: Abstract We consider eigenvalues of the Dirichlet-to-Neumann operator for Laplacian in the domain (or manifold) with edges and establish the asymptotics of the eigenvalue counting function $$N(\lambda )= \kappa _0\lambda ^d +O(\lambda ^{d-1})\qquad \text {as} \lambda \rightarrow +\infty $$ where d is dimension of the boundary. Further, in certain cases we establish two-term asymptotics $$N(\lambda )=\kappa _0\lambda ^d+\kappa _1\lambda ^{d-1}+o(\lambda ^{d-1})\qquad \text {as} \lambda \rightarrow +\infty $$ We also establish improved asymptotics for Riesz means.

Keywords: Dirichlet-to-Neumann operator; spectral asymptotics; 35P20; 58J50 (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-30561-1_31

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DOI: 10.1007/978-3-030-30561-1_31

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