Conditional stability for ill-posed elliptic Cauchy problems : the case of $C^{1,1}$ domains (part I) - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Reports (Research Report) Year : 2008

Conditional stability for ill-posed elliptic Cauchy problems : the case of $C^{1,1}$ domains (part I)

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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Dates and versions

inria-00302354 , version 1 (21-07-2008)

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  • HAL Id : inria-00302354 , version 1

Cite

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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