Abstract
AbstractWe establish interior estimates for Lp‐norms, Orlicz norms, and mean oscillation of second derivatives of solutions to the Monge‐Ampère 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‐Ampère equation in VMO‐type spaces. Our Orlicz estimates also sharpen Caffarelli's celebrated W2, p‐estimates. © 2008 Wiley Periodicals, Inc.
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