学术报告（黄耿耿 5.24）

In this talk, we talk about the regularity of the free boundary in the Monge-Amp\`ere obstacle problem

 \begin{equation}\begin{split}

\det D^2 v= f(y)\chi_{\{v>0\}},\quad \text{in}\quad \Omega\\v=v_0,\quad \text{on}\quad \partial\Omega.

\end{split}

\end{equation}

Assume that $\Omega$ is a bounded convex domain in $\Bbb R^n$, and $f, v_0>0$.Then $\Gamma=\partial \{v=0\}$ is smooth if $f$ is smooth; and $\Gamma$ is analytic if $f$ is analytic. This is a joint work with Prof. Tang Lan and Prof. Wang Xu-Jia.