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Sharp regularity results on second derivatives of solutions to the Monge‐Ampère equation with VMO type data
Abstract We establish interior estimates for L p ‐norms, Orlicz norms, and mean oscillation of second derivatives of solutions to the Monge‐Ampère equation det D 2 u = f ( x ) with zero boundary value, where f ( x ) is strictly positive, bounded, and satisfies a VMO‐type condition. …