Hung V. Tran

Quantitative homogenization of Monge-Amp\`ere equations in periodic media

Let $u^\varepsilon$ and $u$ be the convex solutions of \[ \det D^2u^\varepsilon=F(x,x/\varepsilon),\qquad \det D^2u=\overline F(x) \] on a bounded convex domain $\Omega$, with the same Dirichlet data. Here, $F$ is uniformly positive and periodic in its second variable, and $\overline F(x)=\int_{\mathbb T^n}F(x,y)\,dy$....