Global boundedness of the gradient for a class of nonlinear elliptic   systems
  Gradient boundedness up to the boundary for solutions to Dirichlet and Neumann problems for elliptic systems with Uhlenbeck type structure is established. Nonlinearities of possibly non-polynomial type are allowed, and minimal regularity on the data and on the boundary of the domain is assumed. The case of arbitrary bounded convex domains is also included. 
Andrea Cianchi and Vladimir Maz'ya
math.AP