Partial regularity of solutions of fully nonlinear, uniformly elliptic equations



We prove that a viscosity solution of a uniformly elliptic, fully nonlinear equation is C2,α on the complement of a closed set of Hausdorff dimension at most ϵ less than the dimension. The equation is assumed to be C1, and the constant ϵ > 0 depends only on the dimension and the ellipticity constants. The argument combines the W2,ϵ estimates of Lin with a result of Savin on the C2,α regularity of viscosity solutions that are close to quadratic polynomials. © 2012 Wiley Periodicals, Inc.