Bordeline sharp estimates for solutions to nonlinear elliptic problems

A priori estimates for solutions to homogeneous Neumann problems for uniformly elliptic equations in open subsets ­ of R^n are established, with data in the limiting space L^{n\2} or, more generally, in the Lorentz spaces L^{n\2, q}(\Omega). These estimates are optimal as far as either constants or norms are concerned.