Some L_P local estimates related to the solutions of stochastic differential equations and application to stochastic flows

We establish an estimate, related to the solutions of Ito's stochastic differential equation, from which we deduce (via exponential semi-martingales) various properties of the flow associated to the solution of multidimensional stochastic differential equation with Sobolev space valued diffusion coefficient and measurable drift. We extend some results known in the Lipschitz case, such pathwise uniqueness, weak and strong injection and, continuity with respect to the initial data.