BMO estimates for the p-Laplacian

We prove BMO estimates of the inhomogeneous p-Laplace system given by -div (|del u|(p) (2) del u) = div f. We show that f is an element of BMO implies |del u|(p-2)del u is an element of BMO, which is the limiting case of the nonlinear Calderon-Zygmund theory. This extends the work of DiBenedetto and Manfredi (1993) [2], which was restricted to the super-quadratic case p >= 2, to the full case 1 < p < infinity and even more general growth. Moreover, we prove that A(del u) inherits the Campanato and VMO regularity of f. (C) 2011 Elsevier Ltd. All rights reserved.