On Novel Geometric Structures of Laplacian Eigenfunctions in $\mathbb{R}^3$ and Applications to Inverse Problems
type: Item
instance of: scholarly article
title: On Novel Geometric Structures of Laplacian Eigenfunctions in $\mathbb{R}^3$ and Applications to Inverse Problems
zbMATH Open document ID: 1461.35167
DOI: 10.1137/19M1292989
author: Xinlin Cao
author: Hongyu Liu
author: Jun Zou
author: Huai-An Diao
published in: SIAM Journal on Mathematical Analysis
publication date: 2021-03-19T00:00:00Z
full work available at URL: https://arxiv.org/abs/1909.10174
Mathematics Subject Classification ID: 35P05
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 35Q60
zbMATH DE Number: 7326319
zbMATH Keywords: Laplacian eigenfunctions
zbMATH Keywords: geometric structures
zbMATH Keywords: nodal and generalized singular planes
zbMATH Keywords: inverse scattering
zbMATH Keywords: impedance obstacle
zbMATH Keywords: uniqueness
zbMATH Keywords: single far-field pattern
MaRDI profile type: Publication
arXiv ID: 1909.10174
cites work: Determining a sound-soft polyhedral scatterer by a single far-field measurement
cites work: The hot spots problem in planar domains with on hole
cites work: A counterexample to the ``hot spots'' conjecture
cites work: On nodal and generalized singular structures of Laplacian eigenfunctions and applications to inverse scattering problems
cites work: Some recent progress on inverse scattering problems within general polyhedral geometry
cites work: Uniqueness in an inverse scattering problem within non-trapping polygonal obstacles with at most two incoming waves
cites work: Inverse acoustic and electromagnetic scattering theory
cites work: Looking Back on Inverse Scattering Theory
cites work: Q5823354
cites work: Some results on the schiffer conjecture in \(R^2\)
cites work: On generalized Holmgren's principle to the Lamé operator with applications to inverse elastic problems
cites work: Unique continuation from a generalized impedance edge-corner for Maxwell’s system and applications to inverse problems
cites work: Propagation of singularities from singular and infinite points in certain complex-analytic Cauchy problems and an application to the Pompeiu problem
cites work: Geometrical structure of Laplacian eigenfunctions
cites work: Location of hot spots in thin curved strips
cites work: Q5579836
cites work: A global uniqueness for formally determined inverse electromagnetic obstacle scattering
cites work: Schiffer’s conjecture, interior transmission eigenvalues and invisibility cloaking: Singular problem vs. nonsingular problem
cites work: Stable determination of sound-hard polyhedral scatterers by a minimal number of scattering measurements
cites work: Mosco convergence for \(H(\text{curl})\) spaces, higher integrability for Maxwell's equations, and stability in direct and inverse EM scattering problems
cites work: Uniqueness in an inverse acoustic obstacle scattering problem for both sound-hard and sound-soft polyhedral scatterers
cites work: On unique determination of partially coated polyhedral scatterers with far field measurements
cites work: Q4953888
cites work: Acoustic and electromagnetic equations. Integral representations for harmonic problems
cites work: Seminar on Differential Geometry. (AM-102)
cites work: Eigenfunctions of the Laplacian on a Riemannian Manifold
description: scientific article; zbMATH DE number 7326319