  In this paper we present a new method for the construction of strong
solutions of SDE's with merely integrable drift coefficients driven by a
multidimensional fractional Brownian motion with Hurst parameter H < 1/2.
Furthermore, we prove the rather surprising result of the higher order Frechet
differentiability of stochastic flows of such SDE's in the case of a small
Hurst parameter. In establishing these results we use techniques from Malliavin
calculus combined with new ideas based on a "local time variational calculus".
We expect that our general approach can be also applied to the study of certain
types of stochastic partial differential equations as e.g. stochastic
conservation laws driven by rough paths.
