  The Dirichlet problem for a class of quasilinear elliptic systems of
equations with small-BMO coefficients in Reifenberg-flat domain is considered.
  The lower order terms supposed to satisfy controlled growth conditions. It is
obtained Lp-integrability with p>2 of the gradient of the solution where p
depends explicitly on the data. An analogous result is obtained also for the
Cauchy-Dirichlet problem for quasilinear parabolic systems.
