By employing the Green function, in this paper we provide a new and elementary proof for the interior regularity of solutions to the Monge–Ampère equation. This proof also applies to the complex Monge–Ampère equation and the $k$-Hessian equation.

中文翻译：

---

Monge–Ampère型方程正则性的新证明

通过采用格林函数，本文为蒙格－安培方程的解的内部正则性提供了新的基本证明。该证明也适用于复杂的蒙格-安培方程和$ k $ -Hessian方程。