Eigenvalues of the Laplacian with Neumann boundary conditions

DOI10.1017/S0334270000004525zbMath0567.35067OpenAlexW2142956820MaRDI QIDQ3682906

H. P. W. Gottlieb

Publication date: 1985

Published in: The Journal of the Australian Mathematical Society. Series B. Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0334270000004525

zbMATH Keywords

asymptotic expansionsspectral functionLaplacianNeumann and mixed Dirichlet and Neumann conditions

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (41)

On hearing the shape of the three-dimensional multi-connected vibrating membrane with piecewise smooth boundary conditions ⋮ Reducing dimensionality to model 2D rotating and standing waves in a delayed nonlinear optical system with thin annulus aperture ⋮ 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 ⋮ Estimates for the first eigenvalue for p-Laplacian with mixed boundary conditions ⋮ On hearing the shape of rectilinear regions ⋮ A novel approach to investigate the stability analysis and the dynamics of reaction-diffusion SVIR epidemic model ⋮ An inverse problem for a general multiply connected bounded domain ⋮ Higher dimensional inverse problem for a multi-connected bounded domain with piecewise smooth Robin boundary conditions and its physical applications. ⋮ The wave equation approach to an inverse problem for a general multi-connected domain in \(\mathbb{R}^{2}\) with mixed boundary conditions. ⋮ Inverse problems for a general multi-connected bounded drum with applications in physics. ⋮ The wave equation approach for solving inverse eigenvalue problems of a multi-connected region in \({\mathbb R}^{3}\) with Robin conditions. ⋮ Heat equation for an arbitrary doubly-connected region in \(R^ 2\) with mixed boundary conditions ⋮ An inverse problem for a general doubly connected bounded domain in R³with a Finite Number of Piecewise Impedance Boundary Conditions ⋮ Asymptotic expansions of the heat kernel of the Laplacian for general annular bounded domains with Robin boundary conditions: Further results. ⋮ On the zeros of cross-product Bessel functions in oblique derivative boundary-value problems ⋮ Eigenvalues of the negative Laplacian for simply connected bounded domains ⋮ An inverse problem of the three-dimensional wave equation for a general annular vibrating membrane with piecewise smooth boundary conditions. ⋮ Short-time asymptotics of the two-dimensional wave equation for an annular vibrating membrane with applications in the mathematical physics ⋮ Hearing the shape of a general doubly-connected domain in \(\mathbb{R}^ 3\) with mixed boundary conditions ⋮ 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 ⋮ Short-time asymptotics of the heat kernel on bounded domain with piecewise smooth boundary conditions and its applications to an ideal gas ⋮ An inverse problem of the heat equation for a general multi-connected drum with applications in physics. ⋮ Higher dimensional inverse problem of the wave equation for a bounded domain with mixed boundary conditions ⋮ Hearing the shape of a general convex domain ⋮ Nonlinear principal components. I: Absolutely continuous random variables with positive bounded densities ⋮ Heat equation for a general convex domain inR³with a finite number of piecewise impedance boundary conditions ⋮ Hearing the shape of a general doubly connected domain in R3 with impedance boundary conditions ⋮ Short—time Asymptotics of the Heat Kernel of the Laplacian for a Multiply-connected Domain inR²with Robin Boundary Conditions ⋮ Stable phase retrieval in infinite dimensions ⋮ The 3D inverse problem of the wave equation for a general multi-connected vibrating membrane with a finite number of piecewise smooth boundary conditions. ⋮ An inverse problem for a general vibrating annular membrane in \(\mathbb R^ 3\) with its physical applications: further results. ⋮ 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. ⋮ An inverse problem for the three-dimensional multi-connected vibrating membrane with 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. ⋮ Higher dimensional inverse problem of the wave equation for a general multi-connected bounded domain with a finite number of smooth mixed boundary conditions. ⋮ An inverse problem of the wave equation for a general annular drum in \({\mathbb R}^3\) with Robin boundary conditions ⋮ The 3D inverse problem for waves with fractal and general annular bounded domain with piecewise smooth Robin boundary ⋮ On the exceptional zeros of cross-products of derivatives of spherical Bessel functions

This page was built for publication: Eigenvalues of the Laplacian with Neumann boundary conditions