Abstract
The approach using the large-M-inequality principle introduced by Acerbi and Mingione [2] has been broadly used in W1,p-regularity theory for nonlinear equations in divergence form. We apply this approach to determine an alternative proof of the local W2,p-estimate for viscosity solutions to the fully nonlinear equations F(D2u,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.
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