Lp-integrability of the gradient of solutions to quasilinear systems   with discontinuous coefficients
  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. 
Lubomira G. Softova
math.AP