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Conditional stability for ill-posed elliptic Cauchy problems : the case of $C^{1,1}$ domains (part I)

Laurent Bourgeois 1
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : This paper is devoted to a conditional stability estimate related to the ill-posed Cauchy problems for the Laplace's equation in domains with $C^{1,1}$ boundary. It is an extension of an earlier result for domains of class $C^\infty$. Our estimate is established by using a global Carleman estimate near the boundary in which the exponential weight depends on the distance function to the boundary. Furthermore, we prove that this stability estimate is nearly optimal and induces a nearly optimal convergence rate for the method of quasi-reversibility to solve the ill-posed Cauchy problems.
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https://hal.inria.fr/inria-00302354
Contributor : Laurent Bourgeois <>
Submitted on : Monday, July 21, 2008 - 2:12:08 PM
Last modification on : Thursday, January 14, 2021 - 11:56:02 AM
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Laurent Bourgeois. Conditional stability for ill-posed elliptic Cauchy problems : the case of $C^{1,1}$ domains (part I). [Research Report] RR-6585, INRIA. 2008. ⟨inria-00302354⟩

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