Electronic Journal of Differential Equations,
Vol. 2016 (2016), No. 168, pp. 1-10.

Title: $C^{2,\alpha}$ estimates and existence results for a nonconcave PDE

Author: Vamsi P. Pingali (Indian Inst. of Science, Bangalore, India)

Abstract:
 We establish $C^{2,\alpha}$ estimates for PDE of the form convex + a sum
 of weakly concave functions of the Hessian, thus generalising a recent
 result of Collins which is in turn inspired by a theorem of Caffarelli
 and Yuan. We apply this result to prove a unique continuation result
 for a generalised Monge-Ampere PDE. Independently, we also prove an
 existence result for a special case.

Submitted July 15, 2015. Published July 04, 2016.
Math Subject Classifications: 35J60, 35J96.
Key Words: Evans-Krylov-Safonov theory; nonconcave equations;
           generalised Monge-Ampere equations.