Yang Zhou

Uniqueness for the Degenerate Monge-Amp\`ere Equation on Arbitrary Bounded Convex Domains

Let $n\ge2$ and let $\Omega\subset\mathbb R^n$ be an arbitrary bounded open convex set. The author prove that, for $p>n$, the Dirichlet problem \[ \det D^2u=(-u)^p\quad\text{in }\Omega, \qquad u=0\quad\text{on }\partial\Omega, \qquad u>0\quad\text{in }\Omega \] has at most one convex Alexandrov solution. The proof is b...