Absence of critical mass densities for a vibrating membrane

DOI10.1007/s00245-008-9055-8zbMath1169.35364OpenAlexW2134904417MaRDI QIDQ836061

Pier Domenico Lamberti

Publication date: 31 August 2009

Published in: Applied Mathematics and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00245-008-9055-8

zbMATH Keywords

eigenvaluesLaplace operatorvibrating membranemass density

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Membranes (74K15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (4)

A few results on permittivity variations in electromagnetic cavities ⋮ Viewing the Steklov Eigenvalues of the Laplace Operator as Critical Neumann Eigenvalues ⋮ Shape perturbation of Grushin eigenvalues ⋮ Steklov-type eigenvalues associated with best Sobolev trace constants: domain perturbation and overdetermined systems

Cites Work

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• Critical points of the symmetric functions of the eigenvalues of the Laplace operator and overdetermined problems
• Extremal eigenvalue problems for composite membranes. I
• Extremal eigenvalue problems for composite membranes. II
• Extremal eigenvalue problems defined for certain classes of functions
• Persistence of eigenvalues and multiplicity in the Dirichlet problem for the Laplace operator on nonsmooth domains
• On certain problems on the maximum and minimum of characteristic values and on the Lyapunov zones of stability
• Elliptic Partial Differential Equations of Second Order
• Symmetry breaking and other phenomena in the optimization of eigenvalues for composite membranes

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