Saddle points and overdetermined problems for the Helmholtz equation

DOI10.1007/BF00942843zbMath0793.35065OpenAlexW2068410894MaRDI QIDQ1315360

N. B. Willms, Graham M. L. Gladwell

Publication date: 7 April 1994

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00942843

zbMATH Keywords

Pompeiu problemoverdetermined problems for the Helmholtz equation

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Overdetermined systems of PDEs with constant coefficients (35N05)

Related Items

A duality theorem for an overdetermined eigenvalue problem ⋮ Overdetermined Neumann boundary value problem in unbounded domains ⋮ Some results related to Schiffer's problem ⋮ Schiffer's problem and an isoperimetric inequality for the first buckling eigenvalue of domains on \(\mathbb S^2\) ⋮ An overdetermined problem for the Helmholtz equation ⋮ Boundary regularity for a family of overdetermined problems for the Helmholtz equation.

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Pompeiu problem revisited
• Extensions of the mountain pass theorem
• Rearrangements and convexity of level sets in PDE
• An inverse spectral theorem and its relation to the Pompeiu problem
• An overdetermined Neumann problem in the unit disk
• Some inequalities between Dirichlet and Neumann eigenvalues
• A partial solution of the Pompeiu problem
• Eigenfunctions and nodal sets
• On the convexity of level lines of the fundamental mode in the clamped membrane problem, and the existence of convex solutions in a related free boundary problem
• Dual variational methods in critical point theory and applications
• A symmetry problem in potential theory
• Analyticity and the Pompeiu problem
• Spectral synthesis and the Pompeiu problem
• Continuation and reflection of solutions of partial differential equations
• Harmonic Analysis and the Pompeiu Problem
• Symmetry Theorems Related to Pompeiu's Problem
• A Symmetry Result Related to Some Overdetermined Boundary Value Problems
• Convexity properties of solutions to some classical variational problems
• Differentiation Under the Integral Sign
• A Complete Description of the Normal Subgroups of Genus One of the Modular Group