Hearing the shape of a general convex domain

DOI10.1016/0022-247X(89)90173-XzbMath0692.35067OpenAlexW2037528488MaRDI QIDQ583490

Elsayed M. E. Zayed

Publication date: 1989

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

Full work available at URL: https://doi.org/10.1016/0022-247x(89)90173-x

zbMATH Keywords

spectral functionconvex domainimpedance condition

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Inverse problems for PDEs (35R30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (14)

An inverse eigenvalue problem of the wave equation for a multi-connected region in \(\mathbb{R}^{2}\) together with three different types of boundary conditions ⋮ The asymptotics of the two-dimensional wave equation for a general multi-connected vibrating membrane with piecewise smooth Robin boundary conditions ⋮ On hearing the shape of rectilinear regions ⋮ The wave equation approach to an inverse problem for a general multi-connected domain in \(\mathbb{R}^{2}\) with mixed boundary conditions. ⋮ Eigenvalues of the negative Laplacian for simply connected bounded domains ⋮ Short-time asymptotics of the two-dimensional wave equation for an annular vibrating membrane with applications in the mathematical physics ⋮ Short—time Asymptotics of the Heat Kernel of the Laplacian for a Multiply-connected Domain inR²with Robin Boundary Conditions ⋮ The asymptotics of the heat semigroup for a general bounded domain with mixed boundary conditions ⋮ An inverse problem of the heat equation for a general multi-connected drum with applications in physics. ⋮ Short—time Asymptotics of the Heat Kernel of the Laplacian for a Multiply-connected Domain inR²with Robin Boundary Conditions ⋮ An inverse problem for a general annular-bounded domain in \(\mathbb R^ 2\) with mixed boundary conditions and its physical applications. ⋮ An inverse problem of the wave equation for a general doubly connected region in \(\mathbb R^2\) with a finite number of piecewise smooth Robin boundary conditions. ⋮ On hearing the shape of a general multi-connected vibrating membrane in \(\mathbb R^2\) with piecewise smooth positive functions in the Robin boundary conditions. ⋮ The 3D inverse problem for waves with fractal and general annular bounded domain with piecewise smooth Robin boundary

Cites Work

• An inverse eigenvalue problem for a general convex domain
• A study of certain Green's functions with applications in the theory of vibrating membranes
• Eigenvalues of the Laplacian with Neumann boundary conditions
• Can One Hear the Shape of a Drum?
• Unnamed Item

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