Uniqueness and stability in an inverse problem for the Schrödinger equation

Lucie Baudouin (1) , Jean-Pierre Puel (1)

1 LMV - Laboratoire de Mathématiques de Versailles

We study a Schrödinger equation, with time dependant potential, set in a bounded domain with Dirichlet boundary data and real valued initial condition We consider the inverse problem of determining the potential when the normal derivative is given on a part of the boundary. The main tool to prove uniqueness and stability of this inverse problem is an appropriate global Carleman estimate.

Mots clés: Inverse problem; Schrödinger equation; Dirichlet boundary conditions.; Dirichlet boundary conditions

Domaines: Equations aux dérivées partielles [math.AP]

Lucie Baudouin, Jean-Pierre Puel. Uniqueness and stability in an inverse problem for the Schrödinger equation. Inverse Problems, 2002, 18 (6), pp.1537-1554. ⟨hal-00143868⟩