# Evans-Krylov theorem

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The Evans-Krylov theorem says that if $u$ is a solution to a uniformly elliptic, fully nonlinear, convex or concave, equation \[ F(D^2 u) = 0 \text{ in } B_1,\] then $u \in C^{2,\alpha}(B_{1/2})$ and there is an estimate \[ \|u\|_{C^{2,\alpha}(B_{1/2})} \leq C \|u\|_{L^\infty(B_1)}, \] where $C$ and $\alpha>0$ depend only on the ellipticity constants and dimension.

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