Carleman estimates for stratified media

Assia Benabdallah (1) , Yves Dermenjian (1) , Jérôme Le Rousseau (2, 3)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités
2 FDP - Fédération de recherche Denis Poisson
3 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

We consider anisotropic elliptic and parabolic operators in a bounded stratified media in $\R^n$ characterized by discontinuties of the coefficients in one direction. The surfaces of discontinuities cross the boundary of the domain. We prove Carleman estimates for these operators with an arbitrary observation region.

Mots clés: Elliptic operators; Parabolic operators; Non-smooth coefficients; Stratified media; Carleman estimate; Observation location

Domaines: Equations aux dérivées partielles [math.AP]

Assia Benabdallah, Yves Dermenjian, Jérôme Le Rousseau. Carleman estimates for stratified media. Journal of Functional Analysis, 2011, 260, pp.3645-3677. ⟨10.1016/j.jfa.2011.02.007⟩. ⟨hal-00529924v2⟩