Jordan chains of elliptic partial differential operators and Dirichlet-to-Neumann maps

Let \Omega \subset \mathbb{R}^d be a bounded open set with Lipschitz boundary \Gamma . It will be shown that the Jordan chains of m-sectorial second-order elliptic partial differential operators with measurable coefficients and (local or non-local) Robin boundary conditions in L_2(\Omega) can be cha...

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Bibliographic Details
Published inJournal of spectral theory Vol. 11; no. 3; pp. 1081 - 1105
Main Authors Behrndt, Jussi, ter Elst, A. F. M.
Format Journal Article
LanguageEnglish
Published European Mathematical Society Publishing House 01.01.2021
Subjects
Differential equations, Partial
Eigenvectors
Mathematical research
Austria
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ISSN1664-039X
1664-0403
DOI10.4171/jst/366

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Summary:Let \Omega \subset \mathbb{R}^d be a bounded open set with Lipschitz boundary \Gamma . It will be shown that the Jordan chains of m-sectorial second-order elliptic partial differential operators with measurable coefficients and (local or non-local) Robin boundary conditions in L_2(\Omega) can be characterized with the help of Jordan chains of the Dirichlet-to-Neumann map and the boundary operator from H^{1/2}(\Gamma) into H^{-1/2}(\Gamma) . This result extends the Birman–Schwinger principle in the framework of elliptic operators for the characterization of eigenvalues, eigenfunctions and geometric eigenspaces to the complete set of all generalized eigenfunctions and algebraic eigenspaces.
ISSN:1664-039X
1664-0403
DOI:10.4171/jst/366