Carleman estimates for some non smooth anisotropic media - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2012

Carleman estimates for some non smooth anisotropic media

Résumé

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.
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Dates et versions

hal-00715108 , version 1 (06-07-2012)

Identifiants

  • HAL Id : hal-00715108 , version 1

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Assia Benabdallah, Yves Dermenjian, Laetitia Thevenet. Carleman estimates for some non smooth anisotropic media. 2012. ⟨hal-00715108⟩
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