We consider a stochastic differential equation, driven by a Brownian motion, with non Lipschitz coefficients. We consider the class
which is larger than Sobolev space and got a sufficient condition for a solution of stochastic differential equation to belong to the class
. As a consequence we prove that the corresponding flow is, almost surely, almost every where derivable with respect to initial data. The result is a partial extension of the result of N. Bouleau and F. Hirsch on the derivability, with respect to the initial data, of the solution of a stochastic differential equation with Lipschitz coefficients.
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