Probabilistic approach to the Dirichlet problem of second order elliptic PDE (Q581936)

The author considers the Dirichlet problm for a Schrödinger equation of the type \[ [\sum (a_{ij}\partial /\partial x_ j)_ i+\sum b^ i(\partial /\partial x_ i)+\xi]u=0. \] MA considered this problem but without the drift term. The space \(H^ 2_ 0\) does not seem to be defined in the paper. The reviewer is unable to reconcile theorem 1.7. with the standard definition of the Sobolev space \(H^ 2_ 0\).