Asymptotic properties of the magnetic integrated density of states.
Asymptotics and estimates of the convergence rate in a three-dimensional boundary value problem with rapidly alternating boundary conditions.
Asymptotics of the integrated density of states for periodic elliptic pseudo-differential operators in dimension one.
We consider a periodic pseudo-differential operator on the real line, which is a lower-order perturbation of an elliptic operator with a homogeneous symbol and constant coefficients. It is proved that the density of states of such an operator admits a complete asymptotic expansion at large energies. A few first terms of this expansion are found in a closed form.
Asymptotics of the scattering frequencies for a thermoelasticity problem with small thermal conductivity
Asymptotics of the spectral function for the Steklov problem in a family of sets with fractal boundaries.
Asymptotique des résonances pour des obstacles
Asymptotiques spectrales pour l'opérateur de Schrödinger avec un potentiel électromagnétique
Beyond the classical Weyl and Colin de Verdière’s formulas for Schrödinger operators with polynomial magnetic and electric fields
We present a pair of conjectural formulas that compute the leading term of the spectral asymptotics of a Schrödinger operator on with quasi-homogeneous polynomial magnetic and electric fields. The construction is based on the orbit method due to Kirillov. It makes sense for any nilpotent Lie algebra and is related to the geometry of coadjoint orbits, as well as to the growth properties of certain “algebraic integrals,” studied by Nilsson. By using the direct variational method, we prove that the...
Boltzmann distributed quantum steady states and their classical limit.
Bornes inférieurs pour des fonctions propres de l'opérateur de Schrödinger
Boundary Behaviour of Dirchlet Eigenfunctions of Second Order Elliptic Operators.
Boundary controllability of a chain of serially connected Euler-Bernoulli beams with interior masses.
Boundary feedback stabilization of a hybrid PDE-ODE system.
Bounded nonlinear perturbations of second order linear elliptic problems
Champs magnétiques classiques et quantiques
Comparing heat operators through local isometries or fibrations
Complete asymptotic expansions for eigenvalues of Dirichlet laplacian in thin three-dimensional rods
We consider the Dirichlet Laplacian in a thin curved three-dimensional rod. The rod is finite. Its cross-section is constant and small, and rotates along the reference curve in an arbitrary way. We find a two-parametric set of the eigenvalues of such operator and construct their complete asymptotic expansions. We show that this two-parametric set contains any prescribed number of the first eigenvalues of the considered operator. We obtain the complete asymptotic expansions for the eigenfunctions...
Complete asymptotic expansions for eigenvalues of Dirichlet Laplacian in thin three-dimensional rods*
We consider the Dirichlet Laplacian in a thin curved three-dimensional rod. The rod is finite. Its cross-section is constant and small, and rotates along the reference curve in an arbitrary way. We find a two-parametric set of the eigenvalues of such operator and construct their complete asymptotic expansions. We show that this two-parametric set contains any prescribed number of the first eigenvalues of the considered operator. We obtain the complete asymptotic expansions for the eigenfunctions...
Complexified quantum rules
Comportement asymptotique de la fonction spectrale de l'opérateur de Laplace-Beltrami sur une variété ayant des singularités coniques