Partial regularity of solutions of fully nonlinear uniformly elliptic equations

الأصل · EN

We prove that a viscosity solution of a uniformly elliptic, fully nonlinear equation is C²,α on the compliment 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 which are close to quadratic polynomials.