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<p>In this paper, we study the complex Monge–Ampère equations for unbounded plurifinely plurisubharmonic functions in plurifinely hyperconvex domains. We prove the relationship between the solutions and sub-solutions of the equation for measures with a singular part. As an application, we prove uniqueness of a solution.</p>

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Solutions of Complex Monge–Ampère Equations for Plurifinely Plurisubharmonic Functions

  • 期刊论文

  • 发表日期：

    2026年1月24日

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  • Hoang Van Can,
  • Nguyen Thi Lien,
  • Nguyen Duc Hung

摘要

In this paper, we study the complex Monge–Ampère equations for unbounded plurifinely plurisubharmonic functions in plurifinely hyperconvex domains. We prove the relationship between the solutions and sub-solutions of the equation for measures with a singular part. As an application, we prove uniqueness of a solution.