Spectral analysis of selfadjoint elliptic differential operators, Dirichlet-to-Neumann maps, and abstract Weyl functions

DOI10.1016/j.aim.2015.08.016zbMath1344.47018arXiv1404.0922OpenAlexW2963146369MaRDI QIDQ887334

Jonathan Rohleder, Jussi Behrndt

Publication date: 28 October 2015

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1404.0922

zbMATH Keywords

spectral analysisWeyl functionsymmetric operatorDirichlet-to-Neumann mapelliptic differential operatorboundary triplelocal simplicity condition

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Sturm-Liouville theory (34B24) Spectrum, resolvent (47A10) Weyl theory and its generalizations for ordinary differential equations (34B20) Linear symmetric and selfadjoint operators (unbounded) (47B25)

Related Items (15)

Scattering matrices and Dirichlet-to-Neumann maps ⋮ Dirichlet-to-Neumann maps, abstract Weyl-Titchmarsh \(M\)-functions, and a generalized index of unbounded meromorphic operator-valued functions ⋮ Spectral enclosures for non-self-adjoint extensions of symmetric operators ⋮ Effective behaviour of critical-contrast PDEs: micro-resonances, frequency conversion, and time dispersive properties. I ⋮ Spectral transition for Dirac operators with electrostatic \(\delta\)-shell potentials supported on the straight line ⋮ Global well-posedness of an initial-boundary value problem of the 2-D incompressible Navier-Stokes-Darcy system ⋮ Global well-posedness of coupled Navier-Stokes and Darcy equations ⋮ Self-adjoint Dirac operators on domains in \(\mathbb{R}^3\) ⋮ On the eigenvalues of spectral gaps of elliptic PDEs on waveguides ⋮ The Dirichlet-to-Neumann map for Schrödinger operators with complex potentials ⋮ Donoghue-type \(m\)-functions for Schrödinger operators with operator-valued potentials ⋮ Self-adjoint indefinite Laplacians ⋮ Inverse problems with partial data for elliptic operators on unbounded Lipschitz domains ⋮ Boundary integral formulations of eigenvalue problems for elliptic differential operators with singular interactions and their numerical approximation by boundary element methods ⋮ Jordan chains of elliptic partial differential operators and Dirichlet-to-Neumann maps

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