About stability and regularization of ill-posed elliptic Cauchy problems: The case of C1,1 domains

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 of [Phung, ESAIM: COCV 9 (2003) 621-635] for domains of class C∞. Our estimate is established by using a 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 introduced in [Lattès and Lions, Dunod (1967)] to solve the ill-posed Cauchy problems. © EDP Sciences, SMAI, 2010.
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ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2010, 44 (4), pp.715-735. 〈10.1051/m2an/2010016〉
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Soumis le : mardi 15 octobre 2013 - 10:50:48
Dernière modification le : jeudi 11 janvier 2018 - 06:20:23

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Laurent Bourgeois. About stability and regularization of ill-posed elliptic Cauchy problems: The case of C1,1 domains. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2010, 44 (4), pp.715-735. 〈10.1051/m2an/2010016〉. 〈hal-00873056〉

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