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Article Dans Une Revue Communications in Partial Differential Equations Année : 2013

Carleman Estimates for Some Non-Smooth Anisotropic Media

Résumé

Let B be a n × n block diagonal matrix in which the first block C τ 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 R n. If S denotes the set where discontinuities of C τ 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 ⊂ R n−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-01164681 , version 1 (17-06-2015)

Identifiants

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Assia Benabdallah, Yves Dermenjian, Laetitia Thevenet. Carleman Estimates for Some Non-Smooth Anisotropic Media. Communications in Partial Differential Equations, 2013, pp.Comm. Partial Differential Equations 38 (2013), no. 10, 1763-1790. ⟨10.1080/03605302.2013.804552⟩. ⟨hal-01164681⟩
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