Comportement semi-classique du spectre des hamiltoniens quantiques hypoelliptiques
Comportement semi-classique du spectre des hamiltoniens quantiques elliptiques
Dans cet article nous généralisons les résultats obtenus par J. Chazarain sur le spectre d’opérateurs de Schrödinger lorsque . Nous étendons ses résultats aux opérateurs pseudo-différentiels globalement elliptiques d’ordre .
Composition and L²-boundedness of flag kernels
We prove the composition and L²-boundedness theorems for the Nagel-Ricci-Stein flag kernels related to the natural gradation of homogeneous groups.
Compositions of pseudo-differential operators
Cônes symplectiques et opérateurs de Toeplitz
Conjoint spectral asymptotics for the families of commuting operators and for operators with the periodic hamiltonian flow
Construction de paramétrixes pour des opérateurs pseudodifférentiels caractéristiques sur la réunion de deux cônes lissés
Construction de solutions nulles et singulières pour des opérateurs de type principal
Construction d'un inverse et propagation de la régularité des solutions pour un problème de Dirichlet hyperbolique
Construction of Sobolev spaces of fractional order with sub-riemannian vector fields
Given a smooth family of vector fields satisfying Chow-Hörmander’s condition of step 2 and a regularity assumption, we prove that the Sobolev spaces of fractional order constructed by the standard functional analysis can actually be “computed” with a simple formula involving the sub-riemannian distance.Our approach relies on a microlocal analysis of translation operators in an anisotropic context. It also involves classical estimates of the heat-kernel associated to the sub-elliptic Laplacian.
Continuité-Sobolev de certains opérateurs paradifférentiels.
L'objet de ce travail est l'étude de la continuité des opérateurs d'intégrales singulières (au sens de Calderón-Zygmund) sur les espaces de Sobolev Hs. Il complète le travail fondamental de David-Journé [6], concernant le cas s = 0, et ceux de P. G. Lemarié [10] et M. Meyer [11] concernant le cas 0 < s < 1.
Continuity of solutions of a quasilinear hyperbolic equation with hysteresis
This paper is devoted to the investigation of quasilinear hyperbolic equations of first order with convex and nonconvex hysteresis operator. It is shown that in the nonconvex case the equation, whose nonlinearity is caused by the hysteresis term, has properties analogous to the quasilinear hyperbolic equation of first order. Hysteresis is represented by a functional describing adsorption and desorption on the particles of the substance. An existence result is achieved by using an approximation of...
Contribution of noncommutative geometry to index theory on singular manifolds
This survey of the work of the author with several collaborators presents the way groupoids appear and can be used in index theory. We define the general tools, and apply them to the case of manifolds with corners, ending with a topological index theorem.
Control of a system governed by Dirichlet problem
Contrôle et stabilisation pour l'équation des ondes
Controllability of a parabolic system with a diffuse interface
We consider a linear parabolic transmission problem across an interface of codimension one in a bounded domain or on a Riemannian manifold, where the transmission conditions involve an additional parabolic operator on the interface. This system is an idealization of a three-layer model in which the central layer has a small thickness . We prove a Carleman estimate in the neighborhood of the interface for an associated elliptic operator by means of partial estimates in several microlocal regions....
Convergence dans le domaine complexe des séries de fonctions propres
Correction to "Composition and L²-boundedness of flag kernels" (Colloq. Math. 118 (2010), 581-585)
Cutting the loss of derivatives for solvability under condition
For a principal type pseudodifferential operator, we prove that condition implies local solvability with a loss of 3/2 derivatives. We use many elements of Dencker’s paper on the proof of the Nirenberg-Treves conjecture and we provide some improvements of the key energy estimates which allows us to cut the loss of derivatives from for any (Dencker’s most recent result) to 3/2 (the present paper). It is already known that condition doesnotimply local solvability with a loss of 1 derivative,...