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
Barta's Inequalities and the First Eigenvalue of a Cap Domain of a 2-Sphere.
Basic compactness properties of nonconforming and hybrid finite element spaces
Beispiele für ... auf kompakten Mannigfaltigkeiten.
Bifurcation for nonlinear elliptic boundary value problems I.
This paper is devoted to local static bifurcation theory for a class of degenerate boundary value problems for nonlinear second-order elliptic differential operators. The purpose of this paper is twofold. The first purpose is to prove that the first eigenvalue of the linearized boundary value problem is simple and its associated eigenfunction is positive. The second purpose is to discuss the changes that occur in the structure of the solutions as a parameter varies near the first eigenvalue of the...
Borne inférieure du spectre de l'opérateur de Schrödinger
Bornes inférieurs pour des fonctions propres de l'opérateur de Schrödinger
Bound states of a converging quantum waveguide
We consider a two-dimensional quantum waveguide composed of two semi-strips of width 1 and 1 − ε, where ε > 0 is a small real parameter, i.e. the waveguide is gently converging. The width of the junction zone for the semi-strips is 1 + O(√ε). We will present a sufficient condition for the existence of a weakly coupled bound state below π2, the lower bound of the continuous spectrum. This eigenvalue in the discrete spectrum is unique and its asymptotics is constructed and justified when ε → 0+....
Boundary behavior and estimates for solutions of equations containing the -Laplacian.
Boundary problems of the second order with an indefinite weight-function.
Bounds for the first Dirichlet eigenvalue of triangles and quadrilaterals
We prove some new upper and lower bounds for the first Dirichlet eigenvalue of triangles and quadrilaterals. In particular, we improve Pólya and Szegö's [Annals of Mathematical Studies 27 (1951)] lower bound for quadrilaterals and extend Hersch's [Z. Angew. Math. Phys. 17 (1966) 457–460] upper bound for parallelograms to general quadrilaterals.
Bounds on Schrödinger operators and generalized Sobolev type inequalities
Cheeger's inequality with a boundary term.