Carleman estimates for anisotropic elliptic operators with jumps at an interface

Jérôme Le Rousseau (1, 2, 3) , Nicolas Lerner (4)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
2 FDP - Fédération de recherche Denis Poisson
3 IUF - Institut universitaire de France
4 IMJ - Institut de Mathématiques de Jussieu

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 sharp.

Mots clés: Carleman estimate; Elliptic operator; Non-smooth coefficient; Quasi-mode

Domaines: Equations aux dérivées partielles [math.AP]

Jérôme Le Rousseau, Nicolas Lerner. Carleman estimates for anisotropic elliptic operators with jumps at an interface. Anal. PDE, 2013, 6 (7), pp.1601-1648. ⟨10.2140/apde.2013.6.1601⟩. ⟨hal-00546869v2⟩