Another step toward the solution of the pompeiu problem in the plane

DOI10.1080/03605309308820938zbMath0818.35136OpenAlexW2024647616MaRDI QIDQ4203504

Nicola Garofalo, Fausto Segala

Publication date: 5 September 1993

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605309308820938

zbMATH Keywords

Pompeiu problemPompeiu property

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Inverse problems for PDEs (35R30) Boundary value and inverse problems for harmonic functions in two dimensions (31A25)

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An inverse problem for the equation \(\Delta u=-cu-d\), A duality theorem for an overdetermined eigenvalue problem, Symmetry theorems for the overdetermined eigenvalue problems, ON THE INCOMPRESSIBLE LIMIT FOR THE NAVIER–STOKES–FOURIER SYSTEM IN DOMAINS WITH WAVY BOTTOMS, The pompeiu problem, Some results related to Schiffer's problem, Flattening results for elliptic PDEs in unbounded domains with applications to overdetermined problems, Univalent Functions and the Pompeiu Problem, A new result on the Pompeiu problem, Stability of the convex Pompeiu sets, Boundary regularity for a family of overdetermined problems for the Helmholtz equation.

Cites Work

• An inverse spectral theorem and its relation to the Pompeiu problem
• A note on the Pompeiu problem for convex domains
• Asymptotic expansions for a class of Fourier integrals and applications to the Pompeiu problem
• A partial solution of the Pompeiu problem
• Analyticity and the Pompeiu problem
• Spectral synthesis and the Pompeiu problem
• Seminar on Differential Geometry. (AM-102)
• New Results on the Pompeiu Problem
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