On hearing the shape of rectilinear regions

DOI10.1063/1.530480zbMath0813.35137OpenAlexW2071001196MaRDI QIDQ4317961

A. I. Younis, Elsayed M. E. Zayed

Publication date: 29 January 1995

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.530480

zbMATH Keywords

inverse eigenvalue problemasymptotic expansion of a spectral functioneigenvalues of the negative Laplacian on a bounded domaininformation on the geometry and the boundary conditions

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Inverse problems for PDEs (35R30) Schrödinger operator, Schrödinger equation (35J10)

Related Items (3)

The wave equation approach to an inverse problem for a general multi-connected domain in \(\mathbb{R}^{2}\) with mixed boundary conditions. ⋮ 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. ⋮ The 3D inverse problem for waves with fractal and general annular bounded domain with piecewise smooth Robin boundary

Cites Work

• Hearing the shape of a general convex domain
• Trace formulae for the eigenvalues of the Laplacian
• Heat equation for an arbitrary doubly-connected region in \(R^ 2\) with mixed boundary conditions
• An inverse eigenvalue problem for a general convex domain
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• Hearing the shape of a general doubly-connected domain in \(\mathbb{R}^ 3\) with mixed boundary conditions
• An inverse eigenvalue problem for a general convex domain: an extension to higher dimensions
• A study of certain Green's functions with applications in the theory of vibrating membranes
• Hearing the shape of an annular drum
• Eigenvalues of the Laplacian: an Extension to Higher Dimensions
• Heat Equation for an Arbitrary Multiply-Connected Region in R² with Impedance Boundary Conditions
• An inverse problem for a general convex domain with impedance boundary conditions
• Eigenvalues of the Laplacian with Neumann boundary conditions
• Completeness of the Eigenfunctions of the Equilateral Triangle
• Eigenvalues of the Laplacian for the third boundary value problem
• Heat equation for a general convex domain inR³with a finite number of piecewise impedance boundary conditions
• On hearing the shape of an arbitrary doubly-connected region in R²
• Hearing the shape of a general doubly connected domain in R3 with impedance boundary conditions
• Eigenvalues of the Laplacian for rectilinear regions
• Can One Hear the Shape of a Drum?

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