On local and global structures of transmission eigenfunctions and beyond
DOI10.1515/jiip-2020-0099zbMath1486.35320arXiv2008.03120OpenAlexW3104203518MaRDI QIDQ2122164
Publication date: 6 April 2022
Published in: Journal of Inverse and Ill-Posed Problems (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2008.03120
geometric structuresspectral propertiesinvisibilitytransmission eigenvalue problemsurface localization
Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) General topics in linear spectral theory for PDEs (35P05) Wave scattering in solid mechanics (74J20) Scattering theory for PDEs (35P25) Inverse problems for PDEs (35R30) Completeness of eigenfunctions and eigenfunction expansions in context of PDEs (35P10) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Quantum optics (81V80) Waves and radiation in optics and electromagnetic theory (78A40)
Related Items
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Enhanced multilevel linear sampling methods for inverse scattering problems
- A global uniqueness theorem for an inverse boundary value problem
- Simultaneously recovering potentials and embedded obstacles for anisotropic fractional Schrödinger operators
- Stable determination of sound-hard polyhedral scatterers by a minimal number of scattering measurements
- Corners always scatter
- A neural network scheme for recovering scattering obstacles with limited phaseless far-field data
- Qualitative methods in inverse scattering theory. An introduction
- Full-wave invisibility of active devices at all frequencies
- The interior transmission problem
- Elliptic boundary value problems on corner domains. Smoothness and asymptotics of solutions
- Carleman estimates for coefficient inverse problems and numerical applications.
- Analytic extension and reconstruction of obstacles from few measurements for elliptic second order operators
- On generalized Holmgren's principle to the Lamé operator with applications to inverse elastic problems
- Decoupling elastic waves and its applications
- On an electromagnetic problem in a corner and its applications
- On nodal and generalized singular structures of Laplacian eigenfunctions and applications to inverse scattering problems
- Mosco convergence for \(H(\text{curl})\) spaces, higher integrability for Maxwell's equations, and stability in direct and inverse EM scattering problems
- Recovering a polyhedral obstacle by a few backscattering measurements
- Determining scattering support of anisotropic acoustic mediums and obstacles
- Nearly non-scattering electromagnetic wave set and its application
- On vanishing near corners of transmission eigenfunctions
- Calderón's inverse conductivity problem in the plane
- The Calderón problem with partial data
- Inverse Scattering Theory and Transmission Eigenvalues
- Discreteness of Transmission Eigenvalues via Upper Triangular Compact Operators
- Recovering an electromagnetic obstacle by a few phaseless backscattering measurements
- Regularized Transformation-Optics Cloaking in Acoustic and Electromagnetic Scattering
- Strengthened Linear Sampling Method with a Reference Ball
- The Existence of an Infinite Discrete Set of Transmission Eigenvalues
- Uniqueness Theorems for the Inverse Problem of Acoustic Scattering
- On recovering polyhedral scatterers with acoustic far-field measurements
- On unique determination of partially coated polyhedral scatterers with far field measurements
- Determining both sound speed and internal source in thermo- and photo-acoustic tomography
- A global uniqueness for formally determined inverse electromagnetic obstacle scattering
- Stable determination of sound-soft polyhedral scatterers by a single measurement
- Uniqueness in inverse elastic scattering with finitely many incident waves
- Recovery of polyhedral scatterers by a single electromagnetic far-field measurement
- The Calderón problem with partial data in two dimensions
- Transmission Eigenvalues
- Virtual reshaping and invisibility in obstacle scattering
- Multilevel Linear Sampling Method for Inverse Scattering Problems
- The Denseness of the Far Field Patterns for the Transmission Problem
- Inverse problems and Carleman estimates
- Construction of Corner Singularities for Agmon-Douglis-Nirenberg Elliptic Systems
- Inverse obstacle problem: local uniqueness for rougher obstacles and the identification of a ball
- Approximation by herglotz wave functions
- Uniqueness in an inverse scattering problem within non-trapping polygonal obstacles with at most two incoming waves
- Unique determination of non-smooth sound-soft scatterers by finitely many far-field measurements
- Looking Back on Inverse Scattering Theory
- Nonradiating Sources and Transmission Eigenfunctions Vanish at Corners and Edges
- On isotropic cloaking and interior transmission eigenvalue problems
- On vanishing and localizing of transmission eigenfunctions near singular points: a numerical study
- On Electromagnetic Scattering from a Penetrable Corner
- High-frequency behaviour of corner singularities in Helmholtz problems
- Radiating and non-radiating sources in elasticity
- Determining a sound-soft polyhedral scatterer by a single far-field measurement
- A simple method for solving inverse scattering problems in the resonance region
- On corner scattering for operators of divergence form and applications to inverse scattering
- Electromagnetic interior transmission eigenvalue problem for inhomogeneous media containing obstacles and its applications to near cloaking
- Recovering piecewise constant refractive indices by a single far-field pattern
- Stable determination of polygonal inclusions in Calderón’s problem by a single partial boundary measurement
- On corners scattering stably and stable shape determination by a single far-field pattern
- Uniqueness in determining refractive indices by formally determined far-field data
- Uniqueness in an inverse acoustic obstacle scattering problem for both sound-hard and sound-soft polyhedral scatterers
- On Acoustic Cloaking Devices by Transformation Media and Their Simulation
- Spectral analysis of the interior transmission eigenvalue problem
- Applications of elliptic operator theory to the isotropic interior transmission eigenvalue problem
- Schiffer’s conjecture, interior transmission eigenvalues and invisibility cloaking: Singular problem vs. nonsingular problem
- Reflection principle for the Maxwell equations and its application to inverse electromagnetic scattering
- Zeros of the Bessel and spherical Bessel functions and their applications for uniqueness in inverse acoustic obstacle scattering
- Invisibility and inverse problems
- Inverse acoustic and electromagnetic scattering theory
This page was built for publication: On local and global structures of transmission eigenfunctions and beyond