Classical solutions of fully nonlinear parabolic equations (Q707961)

The authors consider the fully nonlinear equation \(u_t = F(D^2_xu)\). It is well known that if \(u\) is a bounded viscosity solution then \(u\) is a classical solution (i.e. \(u\in C^{2,\alpha}\)) provided that \(F\) is convex (concave). In this paper the authors prove that if \(F\) is \(C^{1,\beta}\) for any \(\beta \in (0,1)\) and \(u\in C^2\) then \(u\in C^{2,\alpha}\) for some \(\alpha \in (0,1)\). They prove this result of interior regularity by using an iteration method.