A nonlinear elliptic system with a transport term and singular data

We consider the nonlinear elliptic system (Formula presented.) where Ω is a bounded, open subset of (Formula presented.), (Formula presented.); (Formula presented.) is a coercive, symmetric matrix with (Formula presented.) coefficients; (Formula presented.) and (Formula presented.) belong to some Lebesgue space, and (Formula presented.) is a continuous function such that (Formula presented.) Using a duality technique, we prove existence of at least a weak solution (Formula presented.). Moreover, if N=3 or N=4, we prove under stronger assumptions on (Formula presented.) and (Formula presented.) that the solution u belongs to (Formula presented.).