W2,p estimates for solutions to asymptotically elliptic equations in nondivergence form

We introduce asymptotically elliptic equations and establish the global W2,pW2,p estimates for viscosity solutions to both asymptotically linear elliptic equations and asymptotically fully nonlinear elliptic equations in bounded domains. Our approach for the proof is based on an appropriate transformation which converts a given asymptotically elliptic equation to a suitable uniformly elliptic equation.