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<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\( \mathbb {C}^n \)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation>. We provide a local version for an existence and uniqueness theorem proved by Darvas et al. (<i>Math. Ann. 379</i>, 95–132, <CitationRef CitationID="CR15">2021</CitationRef>). Our work also extends a result of Åhag et al. (<i>J. Math. Pures Appl. 92</i>, 613–627, <CitationRef CitationID="CR2">2009</CitationRef>).</p>

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

  • 期刊论文

  • 发表日期：

    2025年6月11日

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

摘要

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 \( \mathbb {C}^n \) 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).