BMO estimates for the pp-Laplacian

We prove BMO estimates of the inhomogeneous pp-Laplace system given by −div(|∇u|p−2∇u)=divf. We show that f∈BMO implies |∇u|p−2∇u∈BMO, which is the limiting case of the nonlinear Calderón–Zygmund theory. This extends the work of DiBenedetto and Manfredi (1993) [2], which was restricted to the super-quadratic case p≥2p≥2, to the full case 1