A Dirichlet Type Problem for Non-Pluripolar Complex Monge-Ampère Equations

Abstract

In this paper, we study a Dirichlet type problem for the non-pluripolar complex Monge - Ampère equation with prescribed singularity on a bounded domain of \( \mathbb {C}^n \). We provide a local version for an existence and uniqueness theorem proved by Darvas et al. (Math. Ann. 379, 95–132, 2021). Our work also extends a result of Åhag et al. (J. Math. Pures Appl. 92, 613–627, 2009).