L∞-Estimates for nonlinear elliptic Neumann boundary value problems

In this paper we prove the L-infinity-boundedness of solutions of the quasilinear elliptic equation Au = f(x, u, del u) in Omega, partial derivative u/partial derivative v = g(x, u) on partial derivative Omega, where A is a second order quasilinear differential operator and f : Omega x R x R-N -> R as well as g : partial derivative Omega x R -> R are Caratheodory functions satisfying natural growth conditions. Our main result is given in Theorem 4.1 and is based on the Moser iteration technique along with real interpolation theory. Furthermore, the solutions of the elliptic equation above belong to C-1,C- alpha ((Omega) over bar), if g is Holder continuous.