A Carleman estimate in the neighborhood of a multi-interface and applications to control theory

Rémi Buffe (1, 2, 3)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
2 IECL - Institut Élie Cartan de Lorraine
3 SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization

We prove a Carleman estimate in a neighborhood of a multi-interface, that is, near a point where n manifolds intersect, under compatibility assumptions between the Carleman weight, the operators at the multi-interface, and the elliptic operators in the interior and the usual sub-ellipticity condition. The compatibility condition at the multi-interface is a version of the known covering condition for systems in the literature. This Carleman estimate is a generalization of the results obtained in [6, 7]. Applications in control theory for second-order transmission problems are also considered, and provide a generalization of the known results for one-dimensional networks of strings [4, 13, 19, 30] to higher dimensions.

Mots clés: Carleman estimate; elliptic operators; multiple interfaces; control; stabilization; Lopatinskii condition

Domaines: Equations aux dérivées partielles [math.AP]

Rémi Buffe. A Carleman estimate in the neighborhood of a multi-interface and applications to control theory. 2018. ⟨hal-01703306⟩