Applications of elliptic operator theory to the isotropic interior transmission eigenvalue problem
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Publication:5406711
DOI10.1088/0266-5611/29/10/104003zbMath1285.35059arXiv1212.6785OpenAlexW1968702268MaRDI QIDQ5406711
Evgeny Lakshtanov, Boris Vainberg
Publication date: 2 April 2014
Published in: Inverse Problems (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1212.6785
Dirichlet-to-Neumann mapindex of refractionelliptic operator theoryisotropic interior transmission eigenvalue problem
Scattering theory for PDEs (35P25) Inverse problems for PDEs (35R30) Boundary value problems for second-order elliptic systems (35J57)
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On local and global structures of transmission eigenfunctions and beyond ⋮ The spectral analysis of the interior transmission eigenvalue problem for Maxwell's equations ⋮ Bilaplacian problems with a sign-changing coefficient ⋮ Transmission eigenvalues for strictly concave domains ⋮ Weyl Type Bound on Positive Interior Transmission Eigenvalues ⋮ On vanishing near corners of transmission eigenfunctions ⋮ High-frequency approximation of the interior Dirichlet-to-Neumann map and applications to the transmission eigenvalues ⋮ Sharp Weyl Law for Signed Counting Function of Positive Interior Transmission Eigenvalues ⋮ A note on Sylvester's proof of discreteness of interior transmission eigenvalues ⋮ A boundary integral equation method for the transmission eigenvalue problem ⋮ Counting function for interior transmission eigenvalues ⋮ Improved parametrix in the glancing region for the interior Dirichlet-to-Neumann map ⋮ Weyl asymptotics of the transmission eigenvalues for a constant index of refraction ⋮ Rellich type theorems for unbounded domains ⋮ Radiating and non-radiating sources in elasticity ⋮ Localization of the interior transmission eigenvalues for a ball ⋮ Discreteness of interior transmission eigenvalues revisited ⋮ Transmission eigenvalue-free regions ⋮ Self-adjoint indefinite Laplacians ⋮ Electromagnetic interior transmission eigenvalue problem for an inhomogeneous medium with a conductive boundary ⋮ Non-scattering energies for acoustic-type equations on manifolds with a single flat end ⋮ Boris Rufimovich Vainberg ⋮ Difference Factorizations and Monotonicity in Inverse Medium Scattering for Contrasts with Fixed Sign on the Boundary ⋮ Scattering by Curvatures, Radiationless Sources, Transmission Eigenfunctions, and Inverse Scattering Problems ⋮ On the geometric structures of transmission eigenfunctions with a conductive boundary condition and applications
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