Regularity for a Schrödinger equation with singular potentials and application to bilinear optimal control

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

1 LMV - Laboratoire de Mathématiques de Versailles

We study a Schrödinger equation with a coulombian potential, singular at finite distance, and an electric potential, possibly unbounded. The two potentials are real valued and may depend on space and time variables. We prove that if the electric potential is regular enough and at most quadratic at infinity, this problem is well-posed and the regularity of the initial data is conserved for the solution. We also give an application to the bilinear optimal control of the solution through the electric potential.

Mots clés: Schrödinger equation; singular potential; regularity; existence; bilinear optimal control; optimality condition.; optimality condition

Domaines: Equations aux dérivées partielles [math.AP]

Lucie Baudouin, Otared Kavian, Jean-Pierre Puel. Regularity for a Schrödinger equation with singular potentials and application to bilinear optimal control. Journal of Differential Equations, 2005, 216 (1), pp.188-222. ⟨hal-00145710⟩