Carleman estimates for elliptic operators with jumps at an interface: Anisotropic case and sharp geometric conditions

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

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
2 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 necessary.

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 elliptic operators with jumps at an interface: Anisotropic case and sharp geometric conditions. 2010. ⟨hal-00546869v1⟩