Scattering theory: Some old and new problems.
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Displaying 1 – 11 of 11
Singular values of trilinear forms.
Bernhardsson, Bo, Peetre, Jaak (2001)
Experimental Mathematics
Some functions of eigenvalues of normal operator
Tomáš Kojecký (1990)
Aplikace matematiky
Kellogg's iterations in the eigenvalue problem are discussed with respect to the boundary spectrum of a linear normal operator.
Some new problems in spectral optimization
Giuseppe Buttazzo, Bozhidar Velichkov (2014)
Banach Center Publications
We present some new problems in spectral optimization. The first one consists in determining the best domain for the Dirichlet energy (or for the first eigenvalue) of the metric Laplacian, and we consider in particular Riemannian or Finsler manifolds, Carnot-Carathéodory spaces, Gaussian spaces. The second one deals with the optimal shape of a graph when the minimization cost is of spectral type. The third one is the optimization problem for a Schrödinger potential in suitable classes.
Spectral analysis in a thin domain with periodically oscillating characteristics
Rita Ferreira, Luísa M. Mascarenhas, Andrey Piatnitski (2012)
ESAIM: Control, Optimisation and Calculus of Variations
The paper deals with a Dirichlet spectral problem for an elliptic operator with ε-periodic coefficients in a 3D bounded domain of small thickness δ. We study the asymptotic behavior of the spectrum as ε and δ tend to zero. This asymptotic behavior depends crucially on whether ε and δ are of the same order (δ ≈ ε), or ε is much less than δ(δ = ετ, τ < 1), or ε is much greater than δ(δ = ετ, τ > 1). We consider all three cases.
Spectral analysis in a thin domain with periodically oscillating characteristics
Rita Ferreira, Luísa M. Mascarenhas, Andrey Piatnitski (2012)
ESAIM: Control, Optimisation and Calculus of Variations
The paper deals with a Dirichlet spectral problem for an elliptic operator with ε-periodic coefficients in a 3D bounded domain of small thickness δ. We study the asymptotic behavior of the spectrum as ε and δ tend to zero. This asymptotic behavior depends crucially on whether ε and δ are of the same order (δ ≈ ε), or ε is much less than δ(δ = ετ, τ < 1), or ε is much greater than δ(δ = ετ, τ > 1). ...
Spectral estimates of vibration frequencies of anisotropic beams
Luca Sabatini (2023)
Applications of Mathematics
The use of one theorem of spectral analysis proved by Bordoni on a model of linear anisotropic beam proposed by the author allows the determination of the variation range of vibration frequencies of a beam in two typical restraint conditions. The proposed method is very general and allows its use on a very wide set of problems of engineering practice and mathematical physics.
Spectral properties of non-local uniformly-elliptic operators.
Davidson, Fordyce A., Dodds, Niall (2006)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Spectral study of a coupled compact-noncompact problem
A. Benkaddour, J. Sanchez-Hubert (1992)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Stability of the method of least squares for finding the eigenvalues of a symmetric operator
Karel Najzar (1970)
Commentationes Mathematicae Universitatis Carolinae
Symmetrization of functions and principal eigenvalues of elliptic operators
François Hamel, Nikolai Nadirashvili, Emmanuel Russ (2011/2012)
Séminaire Laurent Schwartz — EDP et applications
In this paper, we consider shape optimization problems for the principal eigenvalues of second order uniformly elliptic operators in bounded domains of . We first recall the classical Rayleigh-Faber-Krahn problem, that is the minimization of the principal eigenvalue of the Dirichlet Laplacian in a domain with fixed Lebesgue measure. We then consider the case of the Laplacian with a bounded drift, that is the operator , for which the minimization problem is still well posed. Next, we deal with...
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