  Let X be the solution of the multidimensional stochastic differential
equationdX(t) = b(t, X(t)) dt + sigma(t, X(t)) dW(t)\, with X(0)=x where W is a
standard Brownian motion. We show that when b is measurable and sigma is in an
appropriate Sobolev space, the law of X satisfies a uniform quadratic
transportation inequality.
