Carleman estimates for elliptic operators with jumps at an interface: Anisotropic case and sharp geometric conditions
Le Rousseau, Jérôme1 ; Lerner, Nicolas2
1 MAPMO, UMR CNRS 6628, Route de Chartres, Université d’Orléans B.P. 6759 – 45067 Orléans cedex 2 France
2 Projet analyse fonctionnelle, Institut de Mathématiques de Jussieu, UMR CNRS 7586, Université Pierre-et-Marie-Curie (Paris 6), Boîte 186 - 4, Place Jussieu - 75252 Paris cedex 05, France
Journées équations aux dérivées partielles (2010), article no. 13, 23 p.

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.

DOI : 10.5802/jedp.70
Mots-clés : Carleman estimate, elliptic operator, non-smooth coefficient, sharp condition, quasi-mode
Le Rousseau, Jérôme 1 ; Lerner, Nicolas 2

1 MAPMO, UMR CNRS 6628, Route de Chartres, Université d’Orléans B.P. 6759 – 45067 Orléans cedex 2 France
2 Projet analyse fonctionnelle, Institut de Mathématiques de Jussieu, UMR CNRS 7586, Université Pierre-et-Marie-Curie (Paris 6), Boîte 186 - 4, Place Jussieu - 75252 Paris cedex 05, France 
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Le Rousseau, Jérôme; Lerner, Nicolas. Carleman estimates for elliptic operators with jumps at an interface: Anisotropic case and sharp geometric conditions. Journées équations aux dérivées partielles (2010), article  no. 13, 23 p. doi : 10.5802/jedp.70. http://www.numdam.org/articles/10.5802/jedp.70/

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