Sharp regularity results on second derivatives of solutions to the Monge-Ampère equation with VMO type data

@inproceedings{Huang2009SharpRR,
  title={Sharp regularity results on second derivatives of solutions to the Monge-Amp{\`e}re equation with VMO type data},
  author={Qingbo Huang},
  year={2009}
}
We establish interior estimates for Lp-norms, Orlicz norms, and mean oscillation of second derivatives of solutions to the Monge-Ampere equation det D2u = f(x) with zero boundary value, where f(x) is strictly positive, bounded, and satisfies a VMO-type condition. These estimates develop the regularity theory of the Monge-Ampere equation in VMO-type spaces. Our Orlicz estimates also sharpen Caffarelli's celebrated W2, p-estimates. © 2008 Wiley Periodicals, Inc. 

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