LAUSR

Abstract The approach using the large-M-inequality principle introduced by Acerbi and Mingione [2] has been broadly used in W 1 , p -regularity theory for nonlinear equations in divergence form. We apply this approach to determine an alternative proof of the local W 2 , p -estimate for viscosity solutions to the fully nonlinear equations F ( D 2 u , x ) = f ( x ) . Using our method, we derive weighted Hessian estimates in variable exponent spaces for the viscosity solutions when nonlinearity F is assumed to be asymptotically convex.