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• W2186077910 abstract "The Dirichlet-to-Neumann operator D! is defined on L 2 (!) where ! is the boundary of a Lipschitz domain and ! a real number which is not an eigenvalue of the Dirichlet Laplacian on L2(). We show that D! is a selfadjoint lower bounded operator with compact resolvent. There is a close connection between its eigenvalues and those of the Laplacian # µ on L 2 () with Robin boundary conditions u = µu|! where µ ! R. This connection is used to generalize L. Friedlander's result ! N+1 ! D ,k =1 ,2 (where ! D is the k # th Dirichlet and ! N the k # th Neumann eigenvalue) to Lipschitz domains. We show that this Euclidean result is false, though, if an arbitrary compact Riemannian manifold M is considered instead of R d and is suitable domain in M." @default.
• W2186077910 created "2016-06-24" @default.
• W2186077910 creator A5022183111 @default.
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• W2186077910 date "2007-01-01" @default.
• W2186077910 modified "2023-09-24" @default.
• W2186077910 title "SPECTRAL PROPERTIES OF THE DIRICHLET-TO-NEUMANN OPERATOR ON LIPSCHITZ DOMAINS" @default.
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