On the Mean Oscillation of the Hessian of Solutions to the Monge-Ampère Equation
We give interior a priori estimates for the mean oscillation of second derivatives of solutions to the Monge-Ampère equation det D2 u = f (x) with zero boundary values, where f (x) is a non-Dini continuous function. If the modulus of continuity of f (x) is φ (r) such that limr → 0 φ (r) log (1 / r) = 0, then D2 u ∈ VMO. © 2005 Elsevier Inc. All rights reserved.
(2006). On the Mean Oscillation of the Hessian of Solutions to the Monge-Ampère Equation. Advances in Mathematics, 207 (2), 599-616.