Carleman Estimates for the Schrödinger Operator. Applications to Quantitative Uniqueness

Laurent Bakri (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

On a closed manifold, we give a quantitative Carleman estimate on the Schrödinger operator. We then deduce quantitative uniqueness results for solutions to the Schrödinger equation using doubling estimates. Finally we investigate the sharpness of this results with respect to the electric potential.

Domaines: Equations aux dérivées partielles [math.AP]

Laurent Bakri. Carleman Estimates for the Schrödinger Operator. Applications to Quantitative Uniqueness. Communications in Partial Differential Equations, 2013, 38 (1), pp.69-91. ⟨10.1080/03605302.2012.736912⟩. ⟨hal-01981180⟩