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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
CNRS - Centre National de la Recherche Scientifique : UMR7231, UMA - Unité de Mathématiques Appliquées, Inria Saclay - Ile de France
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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Submitted on : Monday, July 21, 2008 - 2:12:08 PM
Last modification on : Wednesday, May 11, 2022 - 12:06:04 PM
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  • HAL Id : inria-00302354, version 1


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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