Boundary regularity for a family of overdetermined problems for the Helmholtz equation.

DOI10.1016/S0022-247X(02)00300-1zbMath1049.35081OpenAlexW1993305900MaRDI QIDQ1856855

Stephen A. Williams

Publication date: 11 February 2003

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0022-247x(02)00300-1

Mathematics Subject Classification ID

Boundary values of solutions to elliptic equations and elliptic systems (35J67) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Overdetermined systems of PDEs with constant coefficients (35N05) Solutions to PDEs in closed form (35C05)

Related Items (2)

Qualitative and Numerical Analysis of a Spectral Problem with Perimeter Constraint ⋮ An overdetermined problem for the Helmholtz equation

Cites Work

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• Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains
• An inverse spectral theorem and its relation to the Pompeiu problem
• A note on the Pompeiu problem for convex domains
• A partial solution of the Pompeiu problem
• An introduction to partial differential equations
• On the stability of the spectrum in the Pompeiu problem
• 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
• A duality theorem for an overdetermined eigenvalue problem
• Perturbation of domains in the Pompeiu problem
• Boundary value problems and Hardy spaces associated to the Helmholtz equation in Lipschitz domains
• A symmetry problem in potential theory
• Remark on the preceding paper of Serrin
• Analyticity and the Pompeiu problem
• Spectral synthesis and the Pompeiu problem
• Symmetry Theorems Related to Pompeiu's Problem
• Seminar on Differential Geometry. (AM-102)
• Another step toward the solution of the pompeiu problem in the plane
• The pompeiu problem
• Inverse acoustic and electromagnetic scattering theory

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