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A stability result in the localization of cavities in a thermic conducting medium

B. Canuto, Edi Rosset, S. Vessella (2002)

ESAIM: Control, Optimisation and Calculus of Variations

We prove a logarithmic stability estimate for a parabolic inverse problem concerning the localization of unknown cavities in a thermic conducting medium Ω in n , n 2 , from a single pair of boundary measurements of temperature and thermal flux.

A stability result in the localization of cavities in a thermic conducting medium

B. Canuto, Edi Rosset, S. Vessella (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We prove a logarithmic stability estimate for a parabolic inverse problem concerning the localization of unknown cavities in a thermic conducting medium Ω in n , n ≥ 2, from a single pair of boundary measurements of temperature and thermal flux.

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

Laurent Bourgeois (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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: COCV9 (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...

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