%0 Journal Article
%T About stability and regularization of ill-posed elliptic Cauchy problems: The case of C1,1 domains
%+ Propagation des Ondes : Étude Mathématique et Simulation (POEMS)
%A Bourgeois, Laurent
%< avec comité de lecture
%@ 0764-583X
%J ESAIM: Mathematical Modelling and Numerical Analysis
%I EDP Sciences
%V 44
%N 4
%P 715-735
%8 2010
%D 2010
%R 10.1051/m2an/2010016
%K Carleman estimate
%K distance function
%K elliptic Cauchy problems
%K conditional stability
%K quasi-reversibility
%Z Mathematics Subject Classification: 35A15; 35N25; 35R25; 35R30
%Z Mathematics [math]/Numerical Analysis [math.NA]Journal articles
%X 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.
%G English
%L hal-00873056
%U https://hal-ensta-paris.archives-ouvertes.fr/hal-00873056
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