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Régularité maximale Lp du problème de Cauchy non-autonome et Théorie spectrale des opérateurs de Schrödinger sur les variétés Riemanniennes

Abstract : This thesis is divided into two main parts. The first one is devoted to the maximal regularity of evolution equations. More precisely, given a family of operators, we are interested in the existence and the unicity of a solution to the non-autonomous Cauchy problem. Under a relative continuity hypothesis, we show that the maximal regularity of the family is related to the regularity of each operator. Analogous results are obtained for the second order. In the second part, two problems of spectral theory of Schrödinger operators on manifolds are approached. First of all, we obtain a lower bound for the bottom of the essential spectrum by quantities depending on the potential. We deduce from this result some criterions for the compacity of the resolvant. The last chapter deals with Cwikel-Lieb-Rozenblum type estimate of the number of eigenvalues lying under the essential spectrum. The upper bound that we obtain is directly related to the heat kernel of the Laplacian on the manifold.
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Contributor : César Poupaud <>
Submitted on : Monday, March 20, 2006 - 12:52:04 PM
Last modification on : Thursday, January 11, 2018 - 6:12:18 AM
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César Poupaud. Régularité maximale Lp du problème de Cauchy non-autonome et Théorie spectrale des opérateurs de Schrödinger sur les variétés Riemanniennes. Mathématiques [math]. Université Sciences et Technologies - Bordeaux I, 2005. Français. ⟨tel-00011972⟩

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