Lorentz estimates for fully nonlinear parabolic and elliptic equations

We prove an interior Lorentz estimate of the Hessian of strong solutions to fully nonlinear parabolic equations u(t) + F(D(2)u, x, t) = f(x,t) and elliptic equations F(D(2)u, x) = f(x), respectively. Here, we assume that the associated nonlinearities satisfy uniformly parabolic condition or ellipticity, certain growth condition and the (delta, R)-vanishing condition. We establish Lorentz estimates for such fully nonlinear equations based on the approach of the large-M-inequality principle introduced by Acerbi-Mingione. (C) 2016 Elsevier Ltd. All rights reserved.