\(C^{2,\alpha}\)-estimate for Monge-Ampère equations with Hölder-continuous right hand side (Q258031)

The authors present an alternative proof of the familiar \ \(C^{2,\alpha}\)-estimates for solutions of the Monge-Ampère equations by \textit{M. V. Safonov} [Math. USSR, Izv. 33, No. 3, 597--612 (1989; Zbl 0682.35048); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 52, No. 6, 1272--1287 (1988)] and \textit{L. A. Caffarelli} [Ann. Math. (2) 130, No. 1, 189--213 (1989; Zbl 0692.35017)], and its complex analogue. The proof uses \textit{M. T. Anderson}'s rescaling method [Invent. Math. 102, No. 2, 429--445 (1990; Zbl 0711.53038)] and methods from \textit{X. Chen} et al. [J. Am. Math. Soc. 28, No. 1, 199--234 (2015; Zbl 1312.53097)].