A generalized small perturbation theorem yields interior C^{2,alpha} regularity for nonhomogeneous locally uniformly elliptic equations and measure-zero singular sets for sigma_k(D^2u)=f with positive Lipschitz f.
Caffarelli, Interior C^ 2, regularity theory for a class of nonconvex fully nonlinear elliptic equations , J
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A generalization of Savin's small perturbation theorem for fully nonlinear elliptic equations and applications
A generalized small perturbation theorem yields interior C^{2,alpha} regularity for nonhomogeneous locally uniformly elliptic equations and measure-zero singular sets for sigma_k(D^2u)=f with positive Lipschitz f.