W2,p-Regularity of Lp Viscosity Solutions to Fully Nonlinear Elliptic Equations with Low-Order Terms

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In this paper, we consider the following fully nonlinear elliptic equation F(D2u, Du, x) = f(x), where the operator F satisfies structure condition and the gradient of solution has Lploc growth rate particularly. We employ the technique from geometric tangential analysis whose basic principle is to transfer the good regularity of the recession operator to the original F by approximation methods and establish a prior local W2,p estimates for - Lp-viscosity solutions to the above equation. Mathematics Subject classification (2010): 35B45; 35R05; 35B65.