Interior C2,α regularity theory for a class of nonconvex fully nonlinear elliptic equations

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Universal Moduli of Continuity for Solutions to Fully Nonlinear Elliptic Equations (2011, background): “0 are C2,δ, with appropriate a priori estimates. Evans and Krylov regularity theory, [Ev82] and [K82, K83], assures that convex or concave operators do satisfy (5.1). The work of Cabre and Caﬀarelli, [CC03], provides another class of equations for which one can apply Theorem 5.1. We further mention ”
Elliptic PDE's in probability and geometry: Symmetry and regularity of solutions (2007, background): “The validity of C estimates, or even C estimates, for nonconvex (and nonconcave) operators is still a major open problem —see [12].”
The Bernstein Technique for Integro-Differential Equations (2020, unknown): “5 in [12].”