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Carleman estimates for some non smooth anisotropic media

Assia Benabdallah 1, Yves Dermenjian 1, Laetitia Thevenet 1

(06/2012)

Let B be a n × n block diagonal matrix in which the first block Cτ is an hermitian matrix of order (n − 1) and the second block c is a positive function. Both are piecewise smooth in Ω, a bounded domain of Rn. If S denotes the set where discontinuities of Cτ and c can occur, we suppose that Ω is stratified in a neighborhood of S in the sense that locally it takes the form Ω′ × (−δ, δ) with Ω′ ⊂ Rn−1, δ > 0 and S = Ω′ × {0}. We prove a Carleman estimate for the elliptic operator A = −∇ * (B∇ ) with an arbitrary observation region. This Carleman estimate is obtained through the introduction of a suitable mesh of the neighborhood of S and an associated approximation of c involving the Carleman large parameters.

1 :	Laboratoire d'Analyse, Topologie, Probabilités (LATP)
	CNRS : UMR6632 – Université de Provence - Aix-Marseille I – Université Paul Cézanne - Aix-Marseille III

Domaine

:

Mathématiques/Equations aux dérivées partielles

Mots Clés : anisotropic elliptic operators – approximation – non-smooth coefficients – stratified media – Carleman estimate – observation location.

hal-00715108, version 1

http://hal.archives-ouvertes.fr/hal-00715108

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Contributeur : Assia Benabdallah <>

Soumis le : Vendredi 6 Juillet 2012, 12:51:54

Dernière modification le : Vendredi 6 Juillet 2012, 13:27:54