Singularities of the solution to a certain Cauchy problem and an application to the Pompeiu problem

DOI10.1215/S0012-7094-93-07106-2zbMath0797.35129OpenAlexW1500761796MaRDI QIDQ1312802

Peter Ebenfelt

Publication date: 18 October 1994

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-93-07106-2

zbMATH Keywords

Pompeiu problemoverdetermined Cauchy problemholomorphic Cauchy problem

Mathematics Subject Classification ID

Radon transform (44A12) Laplace transform (44A10) Overdetermined systems of PDEs with constant coefficients (35N05)

Related Items

Harmonic balls and the two-phase Schwarz function, Symmetry theorems for the overdetermined eigenvalue problems, Some results on the schiffer conjecture in \(R^2\), A new result on the Pompeiu problem, Boundary regularity for a family of 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 survey of I. N. Vekua's theory of elliptic partial differential equations with analytic coefficients
• The analytic continuation of solutions of the generalized axially symmetric Helmholtz equation
• Singularities and topology of hypersurfaces
• A partial solution of the Pompeiu problem
• Topological stability of smooth mappings
• Singularities encountered by the analytic continuation of solutions to dirichlet's problem
• On reflection of harmonic functions in surfaces of revolution
• On the dual and hessian mappings of projective hypersurfaces
• Symmetry Theorems Related to Pompeiu's Problem
• Le calcul différentiel et intégral sur une variété analytique complexe. (Problème de Cauchy. III.)
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