A Dirichlet type problem for non-pluripolar complex Monge-Amp\`ere equations

Thai Duong Do; Hoang-Son Do; Van Tu Le; Ngoc Thanh Cong Pham

A Dirichlet type problem for non-pluripolar complex Monge-Amp\`ere equations

Complex Variables 2025-02-06 v2 Analysis of PDEs

Authors: Thai Duong Do , Hoang-Son Do , Van Tu Le , Ngoc Thanh Cong Pham

Abstract

In this paper, we study a Dirichlet type problem for the non-pluripolar complex Monge - Amp\`ere 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, Di Nezza and Lu. Our work also extends a result of Ahag, Cegrell, Czyz and Pham.

Keywords

complex monge-ampère equation dirichlet problem

Cite

@article{arxiv.2407.00937,
  title  = {A Dirichlet type problem for non-pluripolar complex Monge-Amp\`ere equations},
  author = {Thai Duong Do and Hoang-Son Do and Van Tu Le and Ngoc Thanh Cong Pham},
  journal= {arXiv preprint arXiv:2407.00937},
  year   = {2025}
}

Comments

23 pages. In this version, we fixed some minor errors and added some content to the introduction

A Dirichlet type problem for non-pluripolar complex Monge-Amp\`ere equations

Abstract

Keywords

Cite

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