Sobolev inequalities and regularity of the linearized complex Monge-Ampere and Hessian equations

Jiaxiang Wang, Bin Zhou

Let $u$ be a smooth, strictly $k$-plurisubharmonic function on a bounded domain $\Omega \in {\mathbb{C}}^n$ with $2\le k\le n$. The purpose of this paper is to study the regularity of solu…