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The Hypoelliptic Laplacian and Ray-Singer Metrics. (AM-167)
This book presents the analytic foundations to the theory of the hypoelliptic Laplacian. The hypoelliptic Laplacian, a second-order operator acting on the cotangent bundle of a compact manifold, is supposed to interpolate between the classical Laplacian and the geodesic flow. Jean-Michel Bismut and Gilles Lebeau establish the basic functional analytic properties of this operator, which is also studied from the perspective of local index theory and analytic torsion. The book shows that the hypoelliptic Laplacian provides a geometric version of the Fokker-Planck equations. The authors give the proper functional analytic setting in order to study this operator and develop a pseudodifferential c...
Le beau Valentino sort ses crocs
Troisième roman mettant en scène la famille des triplés Antonio, Valentino et Lilli. Valentino est tellement beau que sa mère Alice n'a d'yeux que pour lui. Aussi est-elle emballée par l'idée de le faire participer à une audition. L'expérience s'avère catastrophique et plonge Alice dans une grosse déprime. Jusqu'à ce qu'elle comprenne que Valentino a droit à sa vie et n'a pas à être parfait juste pour lui plaire, à elle qui a tant souffert de ne pas être jolie. -- Portrait caricatural, grinçant et superficiel de la famille, en particulier de la mère envahissante plus à l'écoute d'elle-même que de ses petits; narration banale. [SDM].
Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume I
This monograph explores applications of Carleman estimates in the study of stabilization and controllability properties of partial differential equations, including the stabilization property of the damped wave equation and the null-controllability of the heat equation. All analysis is performed in the case of open sets in the Euclidean space; a second volume will extend this treatment to Riemannian manifolds. The first three chapters illustrate the derivation of Carleman estimates using pseudo-differential calculus with a large parameter. Continuation issues are then addressed, followed by a proof of the logarithmic stabilization of the damped wave equation by means of two alternative proof...
Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume II
This monograph explores applications of Carleman estimates in the study of stabilization and controllability properties of partial differential equations, including quantified unique continuation, logarithmic stabilization of the wave equation, and null-controllability of the heat equation. Where the first volume derived these estimates in regular open sets in Euclidean space and Dirichlet boundary conditions, here they are extended to Riemannian manifolds and more general boundary conditions. The book begins with the study of Lopatinskii-Sapiro boundary conditions for the Laplace-Beltrami operator, followed by derivation of Carleman estimates for this operator on Riemannian manifolds. Appli...
Diffraction by an Immersed Elastic Wedge
This monograph presents the mathematical description and numerical computation of the high-frequency diffracted wave by an immersed elastic wave with normal incidence. The mathematical analysis is based on the explicit description of the principal symbol of the pseudo-differential operator connected with the coupled linear problem elasticity/fluid by the wedge interface. This description is subsequently used to derive an accurate numerical computation of diffraction diagrams for different incoming waves in the fluid, and for different wedge angles. The method can be applied to any problem of coupled waves by a wedge interface. This work is of interest for any researcher concerned with high frequency wave scattering, especially mathematicians, acousticians, engineers.
