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Complex Monge-Ampère Equation in Strictly Pseudoconvex Domains

Acta Mathematica Vietnamica volume 45, pages 93–101 (2020)Cite this article

Abstract

We study the complex Monge-Ampère equation (ddcu)n = μ in a strictly pseudoconvex domain Ω with the boundary condition u = φ, where φ ∈ C(∂Ω). We provide a nontrivial sufficient condition for continuity of the solution u outside “small sets”.

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Funding

This research is funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant no. 101.02-2017.306.

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Authors and Affiliations

  1. Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Hanoi, Vietnam

    Hoang-Son Do, Thai Duong Do & Hoang Hiep Pham

Authors
  1. Hoang-Son Do
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  2. Thai Duong Do
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  3. Hoang Hiep Pham
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Correspondence to Hoang-Son Do.

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In honor of Lê Văn Thiêm’s centenary

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Do, HS., Do, T.D. & Pham, H.H. Complex Monge-Ampère Equation in Strictly Pseudoconvex Domains. Acta Math Vietnam 45, 93–101 (2020). https://doi.org/10.1007/s40306-018-00313-2

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  • DOI: https://doi.org/10.1007/s40306-018-00313-2

Keywords

  • Monge-Ampère equation
  • Pseudoconvex domains
  • Hyperconvex domain

Mathematics Subject Classification (2010)

  • 32U15
  • 32T15
  • 32W20