A counterexample to Schauder estimates for elliptic operators with unbounded coefficients

We consider a homogeneous elliptic Dirichlet problem involving an Ornstein-Uhlenbeck operator in a half space of R^2. We show that for a particular initial datum, which is Lipschitz continuous and bounded, the second derivative of the classical solution is not uniformly continuous. In particular this implies that the well known maximal Holder-regularity results fail in general for Dirichlet problems in unbounded domains involving unbounded coefficients.