Sharp Hessian integrability for the planar Monge--Ampère equation

XiaoRui Lu, Jin Yan, Bao Yu +1

We determine the optimal local integrability of the Hessian for planar convex Alexandrov solutions satisfying $$\lambda dx\le {\mu }_u\le {\lambda }^{-1}dx,0<\lambda <1.$$ The distributional Hes…