Two Methods of Solution of the Three-Dimensional Inverse Nodal Problem.

Yu E. Karpeshina; J. R. McLaughlin

Displaying similar documents to “Two Methods of Solution of the Three-Dimensional Inverse Nodal Problem.”

Localization effects for eigenfunctions near to the edge of a thin domain

Serguei A. Nazarov (2002)

Mathematica Bohemica

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It is proved that the first eigenfunction of the mixed boundary-value problem for the Laplacian in a thin domain $Ω_{h}$ is localized either at the whole lateral surface $Γ_{h}$ of the domain, or at a point of $Γ_{h}$ , while the eigenfunction decays exponentially inside $Ω_{h}$ . Other effects, attributed to the high-frequency range of the spectrum, are discussed for eigenfunctions of the mixed boundary-value and Neumann problems, too.

Singular asymptotic expansions for Dirichlet eigenvalues and eigenfunctions of the laplacian on thin planar domains

Denis Borisov, Pedro Freitas (2009)

Annales de l'I.H.P. Analyse non linéaire

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When is the first eigenfunction for the clamped plate equation of fixed sign?

Sweers, Guido (2001)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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The first bifurcation point for Delaunay nodoids.

Rossman, Wayne (2005)

Experimental Mathematics

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On the nodal set of the second eigenfunction of the laplacian in symmetric domains in $R^{N}$

Lucio Damascelli (2000)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We present a simple proof of the fact that if $Ω$ is a bounded domain in $R^{N}$ , $N \geq 2$ , which is convex and symmetric with respect to $k$ orthogonal directions, $1 \leq k \leq N$ , then the nodal sets of the eigenfunctions of the laplacian corresponding to the eigenvalues $λ_{2}, \dots, λ_{k + 1}$ must intersect the boundary. This result was proved by Payne in the case $N = 2$ for the second eigenfunction, and by other authors in the case of convex domains in the plane, again for the second eigenfunction.

Displaying similar documents to “Two Methods of Solution of the Three-Dimensional Inverse Nodal Problem.”

Localization effects for eigenfunctions near to the edge of a thin domain

Singular asymptotic expansions for Dirichlet eigenvalues and eigenfunctions of the laplacian on thin planar domains

When is the first eigenfunction for the clamped plate equation of fixed sign?

The first bifurcation point for Delaunay nodoids.

On the nodal set of the second eigenfunction of the laplacian in symmetric domains in R N

On the nodal set of the second eigenfunction of the laplacian in symmetric domains in $R^{N}$