A partial solution of the Pompeiu problem

DOI10.1007/BF01360881zbMath0329.35045OpenAlexW2024262872MaRDI QIDQ1227111

Stephen A. Williams

Publication date: 1976

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/162883

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Inverse problems for PDEs (35R30) Overdetermined systems of PDEs with constant coefficients (35N05)

Related Items (34)

An inverse problem for the equation \(\Delta u=-cu-d\) ⋮ On the Pompeiu problem and its generalizations ⋮ A duality theorem for an overdetermined eigenvalue problem ⋮ Heat flow, heat content and the isoparametric property ⋮ The two-sided Pompeiu problem for discrete groups ⋮ 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 ⋮ An identity theorem for the Fourier-Laplace transform of polytopes on nonzero complex multiples of rationally parameterizable hypersurfaces ⋮ The null set of a polytope, and the Pompeiu property for polytopes ⋮ Singularities almost always scatter: Regularity results for non‐scattering inhomogeneities ⋮ Quadrature domains for the Helmholtz equation with applications to non-scattering phenomena ⋮ An inverse spectral theorem and its relation to the Pompeiu problem ⋮ Isoparametric foliations and the Pompeiu property ⋮ A note on the Pompeiu problem for convex domains ⋮ Influence of the hidden regularity on the stability of partially damped systems of wave equations ⋮ Geometry and topology of some overdetermined elliptic problems ⋮ Sets with the Pompeiu property on the plane and on the sphere ⋮ The pompeiu problem ⋮ 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 ⋮ Geometric rigidity of constant heat flow ⋮ A new result on the Pompeiu problem ⋮ The Pompeiu problem on locally symmetric spaces ⋮ Unique continuation property near a corner and its fluid-structure controllability consequences ⋮ Another step toward the solution of the pompeiu problem in the plane ⋮ Stability of the convex Pompeiu sets ⋮ Boundary regularity for a family of overdetermined problems for the Helmholtz equation. ⋮ Singularities of the solution to a certain Cauchy problem and an application to the Pompeiu problem ⋮ 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

Cites Work

• A symmetry problem in potential theory
• Spectral synthesis and the Pompeiu problem
• On the Analyticity of the Solutions of Analytic Non-Linear Elliptic Systems of Partial Differential Equations: Part I. Analyticity in the Interior
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