The Kato smoothing effect for Schr{ö}dinger equations with unbounded potentials in exterior domains

Luc Robbiano (1) , Claude Zuily (2)

1 LMV - Laboratoire de Mathématiques de Versailles
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay

In this paper we prove the smoothing effect for solutions of Schr{ö}dinger equations with variable coefficients and in a non trapping exterior domain. We allow quadratic potentials at infinity.

Mots clés: Schr{ö}dinger equations; Smoothing effect; Boundary problem

Domaines: Equations aux dérivées partielles [math.AP]

Luc Robbiano, Claude Zuily. The Kato smoothing effect for Schr{ö}dinger equations with unbounded potentials in exterior domains. International Mathematics Research Notices, 2009, 9, pp.1636-1698. ⟨hal-00113059⟩