Asymptotic behavior of the ground state of large atoms
Asymptotic behaviour and numerical approximation of optimal eigenvalues of the Robin laplacian
We consider the problem of minimising the nth-eigenvalue of the Robin Laplacian in RN. Although for n = 1,2 and a positive boundary parameter α it is known that the minimisers do not depend on α, we demonstrate numerically that this will not always be the case and illustrate how the optimiser will depend on α. We derive a Wolf–Keller type result for this problem and show that optimal eigenvalues grow at most with n1/N, which is in sharp contrast with the Weyl asymptotics for a fixed domain. We further...
Asymptotic distribution of eigenfrequencies for damped wave equations
Il est bien connu que les fréquences propres associées à un d'Alembertien amorti sont confinées dans une bande parallèle à l'axe réel. Nous rappelons l'asymptotique de Weyl pour la distribution des parties réelles des fréquences propres, nous montrons que «presque toutes» les fréquences propres appartiennent à une bande déterminée par la limite de Birkhoff du coefficient d'amortissement. Nous montrons aussi que certaines moyennes des parties imaginaires convergent vers la moyenne du coefficient...
Asymptotic estimates for bound states in quantum waveguides coupled laterally through a narrow window
Asymptotic lower bounds for eigenvalues by nonconforming finite element methods.
Asymptotics and estimates of the convergence rate in a three-dimensional boundary value problem with rapidly alternating boundary conditions.
Asymptotics of the spectral function for the Steklov problem in a family of sets with fractal boundaries.
Autovalori di un problema ellittico dipendente da un parametro in modo non lineare