Interior $C^{1,\alpha }$ estimates for the linearized Monge--Ampère equation in two dimensions

Ling Wang, Bin Zhou

We prove an interior $C^{1,\alpha }$ estimate for solutions of the homogeneous linearized Monge--Ampère equation in dimension two under the assumption \[ 0<λ\leq \det D^2φ\leqΛ<+\infty.…