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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
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 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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Submitted on : Tuesday, October 15, 2013 - 10:50:48 AM
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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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