Volume 44, Number 4, July-August 2010
|Page(s)||715 - 735|
|Published online||23 February 2010|
About stability and regularization of ill-posed elliptic Cauchy problems: the case of C1,1 domains
Laboratoire POEMS, ENSTA, 32 Boulevard Victor, 75739 Paris Cedex 15, France. email@example.com
Revised: 11 June 2009
This paper is devoted to a conditional stability estimate related to the ill-posed Cauchy problems for the Laplace's equation in domains with C1,1 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.
Mathematics Subject Classification: 35A15 / 35N25 / 35R25 / 35R30
Key words: Carleman estimate / distance function / elliptic Cauchy problems / conditional stability / quasi-reversibility
© EDP Sciences, SMAI, 2010
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.