Regularity of free boundary for the Monge-Ampère obstacle problem (Q6620660)

The article addresses the regularity of free boundaries in the Monge-Ampère obstacle problem, extending results for singular Monge-Ampère equations.\N\NThe authors establish smoothness and analyticity of the free boundary under specific conditions, using a novel approach based on duality and asymptotic analysis. Their method involves transforming the Monge-Ampère equation into a singular, fully nonlinear elliptic equation.\N\NKey results include the derivation of asymptotic estimates near singularities and the proof of regularity for the transformed equations via a series of Legendre transformations and blowup arguments, with extensive use of advanced techniques such as Pogorelov estimates, the maximum principle, and Bernstein-type arguments.