Global C1,α Regularity for Monge-Ampere Equation and Convex Envelope

作者：Caffarelli, Luis A.^*; Tang, Lan; Wang, Xu-Jia

来源：Archive for Rational Mechanics and Analysis, 2022, 244(1): 127-155.

DOI：10.1007/s00205-022-01757-5

• DIRICHLET PROBLEM
• BOUNDARY

In this paper we establish the global C-1,C-alpha regularity for solutions to the Dirichlet problem of the Monge-Ampere equation det D(2)u = f. By examples we show that our conditions are optimal. Our proof allows the degenerate case f >= 0, including the special case f equivalent to 0. We also prove the global C-1,C-alpha regularity for the convex envelope of a given function under optimal conditions.