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Carleman estimates near boundaries, interfaces and for singular problems

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 operators of 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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Submitted on : Thursday, February 22, 2018 - 3:53:12 PM
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  • HAL Id : tel-01715338, version 1

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Rémi Buffe. Carleman estimates near boundaries, interfaces and for singular problems. Equations aux dérivées partielles [math.AP]. Université d'Orléans, 2017. Français. ⟨tel-01715338⟩

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