On the Mean Oscillation of the Hessian of Solutions to the Monge-Ampère Equation

Authors

Qingbo Huang, Wright State UniversityFollow

Document Type

Article

Publication Date

12-20-2006

Abstract

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.

Repository Citation

Huang, Q. (2006). On the Mean Oscillation of the Hessian of Solutions to the Monge-Ampère Equation. Advances in Mathematics, 207 (2), 599-616.
https://corescholar.libraries.wright.edu/math/354

DOI

10.1016/j.aim.2005.12.005