$C^{1,\frac{1}{3}-}$ very weak solutions to the two dimensional Monge-Ampére equation

Wentao Cao, Jonas Hirsch, Dominik Inauen

For any $\theta <\frac{1}{3}$, we show that very weak solutions to the two-dimensional Monge-Ampère equation with regularity $C^{1,\theta }$ are dense in the space of continuous functions. Thi…