The Kato smoothing effect for Schr{\"o}dinger equations with unbounded   potentials in exterior domains
  In this paper we prove the smoothing effect for solutions of Schr{\"o}dinger equations with variable coefficients and in a non trapping exterior domain. We allow quadratic potentials at infinity. 
Luc Robbiano (LM-Versailles), Claude Zuily (LM-Orsay)