An inverse spectral theorem and its relation to the Pompeiu problem

DOI10.1007/BF02797683zbMath0449.35024MaRDI QIDQ1147296

Carlos. A. Berenstein

Publication date: 1980

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

zbMATH Keywords

Dirichlet probleminverse problemsPompeiu propertyinverse spectral theoremover- determined Neumann problem

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Spectral theory and eigenvalue problems for partial differential equations (35P99) Inverse problems for PDEs (35R30) Harmonic analysis in several variables (42B99) Overdetermined problems for partial differential equations and systems of partial differential equations (35N99)

Related Items (43)

A proof via finite elements for Schiffer's conjecture on a regular pentagon ⋮ Approximate controllability for a linear model of fluid structure interaction ⋮ Fourier transform, null variety, and Laplacian's eigenvalues ⋮ An inverse problem for the equation \(\Delta u=-cu-d\) ⋮ A local version of the two-circles theorem ⋮ Energy decay in thermoelastic bodies with radial symmetry ⋮ Some Remarks on the Pompeiu Problem for Groups ⋮ A duality theorem for an overdetermined eigenvalue problem ⋮ Heat flow, heat content and the isoparametric property ⋮ Inverse mean value property of metaharmonic functions ⋮ Symmetry theorems for the overdetermined eigenvalue problems ⋮ Rellich type identities for eigenvalue problems and application to the Pompeiu problem ⋮ Sign-changing solution for an overdetermined elliptic problem on unbounded domain ⋮ The null set of a polytope, and the Pompeiu property for polytopes ⋮ Singularities almost always scatter: Regularity results for non‐scattering inhomogeneities ⋮ On the thermoelasticity with several dissipative mechanisms of type III ⋮ Exponential decay of solutions in type II porous-thermo-elasticity with quasi-static microvoids ⋮ Isoparametric foliations and the Pompeiu property ⋮ A note on the Pompeiu problem for convex domains ⋮ Some results on the schiffer conjecture in \(R^2\) ⋮ The pompeiu problem ⋮ An overdetermined Neumann problem in the unit disk ⋮ Asymptotic expansions for a class of Fourier integrals and applications to the Pompeiu problem ⋮ Some results related to Schiffer's problem ⋮ New Results on the Pompeiu Problem ⋮ Stability results for the \(N\)-dimensional Schiffer conjecture via a perturbation method ⋮ Symmetry results for overdetermined boundary value problems of nonlinear elliptic equations ⋮ Schiffer's problem and an isoperimetric inequality for the first buckling eigenvalue of domains on \(\mathbb S^2\) ⋮ An overdetermined problem for an elliptic equation ⋮ Geometric rigidity of constant heat flow ⋮ Qualitative and Numerical Analysis of a Spectral Problem with Perimeter Constraint ⋮ An inverse problem for an elliptic equation ⋮ Univalent Functions and the Pompeiu Problem ⋮ A new result on the Pompeiu problem ⋮ Deformations of balls in Schiffer's conjecture for Riemannian symmetric spaces ⋮ Inversion of the local Pompeiu transform ⋮ The covariogram and Fourier–Laplace transform in ℂⁿ ⋮ Another step toward the solution of the pompeiu problem in the plane ⋮ Stability of the convex Pompeiu sets ⋮ An overdetermined problem for the Helmholtz equation ⋮ Boundary regularity for a family of overdetermined problems for the Helmholtz equation. ⋮ Saddle points and overdetermined problems for the Helmholtz equation ⋮ Propagation of singularities from singular and infinite points in certain complex-analytic Cauchy problems and an application to the Pompeiu problem

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