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Jérôme Le Rousseau; Nicolas Lerner
Carleman estimates for elliptic operators with jumps at an interface: Anisotropic case and sharp geometric conditions
Journées équations aux dérivées partielles (2010), Exp. No. 13, 23 p., doi: 10.5802/jedp.70
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Mots clés: Carleman estimate; elliptic operator; non-smooth coefficient; sharp condition; quasi-mode

Résumé - Abstract

We consider a second-order selfadjoint elliptic operator with an anisotropic diffusion matrix having a jump across a smooth hypersurface. We prove the existence of a weight-function such that a Carleman estimate holds true. We moreover prove that the conditions imposed on the weight function are necessary.

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