Quasi-linear Stochastic Partial Differential Equations with irregular   Coefficients - Malliavin regularity of the Solutions
  We study quasi-linear stochastic partial differential equations with discontinuous drift coefficients. Existence and uniqueness of a solution is already known under weaker conditions on the drift, but we are interested in the regularity of the solution in terms of Malliavin calculus. We prove that when the drift is bounded and measurable the solution is directional Malliavin differentiable. 
Torstein Nilssen
math.PR