On Novel Geometric Structures of Laplacian Eigenfunctions in $\mathbb{R}^3$ and Applications to Inverse Problems

DOI10.1137/19M1292989zbMath1461.35167arXiv1909.10174MaRDI QIDQ5855623

Jun Zou, Hongyu Liu, Xinlin Cao, Huai-An Diao

Publication date: 19 March 2021

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.10174

zbMATH Keywords

uniquenessgeometric structuresinverse scatteringLaplacian eigenfunctionssingle far-field patternimpedance obstaclenodal and generalized singular planes

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) General topics in linear spectral theory for PDEs (35P05) Scattering theory for PDEs (35P25) Inverse problems for PDEs (35R30)

Related Items (11)

Stable determination by a single measurement, scattering bound and regularity of transmission eigenfunctions ⋮ An inverse problem study related to a fractional diffusion equation ⋮ On a Hybrid Approach for Recovering Multiple Obstacles ⋮ Dependence of eigenvalues of \((2n + 1)\)th order boundary value problems with transmission conditions ⋮ Broad Learning System with Preprocessing to Recover the Scattering Obstacles with Far–Field Data ⋮ Spectral properties of an acoustic-elastic transmission eigenvalue problem with applications ⋮ Geometrical Characterizations of Non-Radiating Sources at Polyhedral and Conical Corners with Applications ⋮ Schwarzschild Harmonic Path Planning and Tetrahedral Mesh Smoothing ⋮ Two single-measurement uniqueness results for inverse scattering problems within polyhedral geometries ⋮ Further results on generalized Holmgren's principle to the Lamé operator and applications ⋮ On invariant properties of natural differential operators associated to geometric structures on \(\mathbb{R}^n\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Some results on the schiffer conjecture in \(R^2\)
• Stable determination of sound-hard polyhedral scatterers by a minimal number of scattering measurements
• The hot spots problem in planar domains with on hole
• A counterexample to the ``hot spots conjecture
• Propagation of singularities from singular and infinite points in certain complex-analytic Cauchy problems and an application to the Pompeiu problem
• Location of hot spots in thin curved strips
• On generalized Holmgren's principle to the Lamé operator with applications to inverse elastic problems
• On nodal and generalized singular structures of Laplacian eigenfunctions and applications to inverse scattering problems
• Some recent progress on inverse scattering problems within general polyhedral geometry
• Mosco convergence for \(H(\text{curl})\) spaces, higher integrability for Maxwell's equations, and stability in direct and inverse EM scattering problems
• Geometrical Structure of Laplacian Eigenfunctions
• Eigenfunctions of the Laplacian on a Riemannian Manifold
• On unique determination of partially coated polyhedral scatterers with far field measurements
• A global uniqueness for formally determined inverse electromagnetic obstacle scattering
• Seminar on Differential Geometry. (AM-102)
• Uniqueness in an inverse scattering problem within non-trapping polygonal obstacles with at most two incoming waves
• Looking Back on Inverse Scattering Theory
• Determining a sound-soft polyhedral scatterer by a single far-field measurement
• Uniqueness in an inverse acoustic obstacle scattering problem for both sound-hard and sound-soft polyhedral scatterers
• Schiffer’s conjecture, interior transmission eigenvalues and invisibility cloaking: Singular problem vs. nonsingular problem
• Unique continuation from a generalized impedance edge-corner for Maxwell’s system and applications to inverse problems
• Inverse acoustic and electromagnetic scattering theory
• Acoustic and electromagnetic equations. Integral representations for harmonic problems

This page was built for publication: On Novel Geometric Structures of Laplacian Eigenfunctions in $\mathbb{R}^3$ and Applications to Inverse Problems