Quasilinear elliptic systems with a drift term: Existence and regularity

We consider a quasilinear system with a drift term of N ≥ 2 equations in a bounded domain Ω⊂Rn with n ≥ 3. Assuming that the support of the off-diagonal coefficients is contained in a crossed staircase of squares with geometrically increasing side lengths, it is proved that weak solutions enjoy Lp -regularity for any p∈[1,+∞). The existence of at least a weak solution is established provided that the Ln -norm of the drift term is sufficiently small. to Gioconda Moscariello on occasion of her birthday