Inégalités de Carleman près du bord, d’une interface et pour des problèmes singuliers

Abstract : In the first part of this thesis, we derive elliptic Carleman estimates for second-order operators with Ventcel boundary conditions. In the second part, we prove a proper estimate near multi-interfaces for elliptic operatorsof any order, under the classical sub-ellipticity condition of Hörmander and under a compatibility condition between the operators in the interior and at the multi-interface, called the covering condition. This condition is a generalization of the well-known Lopatinskii condition. Finally, in the third part, we focus on controllability properties of the heat equation, and stabilization properties of the wave equation for polygonal domains, with mixed boundary conditions.
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Rémi Buffe. Inégalités de Carleman près du bord, d’une interface et pour des problèmes singuliers. Mathématiques générales [math.GM]. Université d'Orléans, 2017. Français. ⟨NNT : 2017ORLE2059⟩. ⟨tel-01985192⟩

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