Optimal bounds for solutions to Neumann problems in limiting cases

A priori estimates for solutions to homogeneous Neumann problems for uniformly elliptic equa- tions in open subsets \Omega­ of IR^n are established when the datum on right-hand side is in the limiting space L^{n/2}(\Omega), 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.