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The Dirichlet Problem for the Complex Monge–Ampère Operator on Strictly Plurifinely Pseudoconvex Domains

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Abstract

In this paper, we are interested in studying the strictly \({\mathcal {F}}\)-pseudoconvex domains and solving the Dirichlet problem of the complex Monge–Ampère operator. We will prove that the solutions can be discontinuous in the usual sense.

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Acknowledgements

The authors would like to thank the referee for valuable remarks that helped to improve the exposition in this paper.

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Author notes

  1. Pham Thi Lieu

    Present address: Pham Thi Lieu, 19/12/1988, Sonha, Phuxuyen, Hanoi, Vietnam

Authors and Affiliations

  1. Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy Street, Cau Giay District, Hanoi, Vietnam

    Nguyen Xuan Hong

  2. Department of Basis Sciences and Foreign Languages, People’s Police University of Technology and Logistics, Thuận Thành, Bacninh, Vietnam

    Pham Thi Lieu

Authors
  1. Nguyen Xuan Hong
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  2. Pham Thi Lieu
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Correspondence to Nguyen Xuan Hong.

Additional information

Communicated by Fabrizio Colombo.

This article is part of the topical collection “Spectral Theory and Operators in Mathematical Physics” edited by Jussi Behrndt, Fabrizio Colombo and Sergey Naboko.

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Hong, N.X., Lieu, P.T. The Dirichlet Problem for the Complex Monge–Ampère Operator on Strictly Plurifinely Pseudoconvex Domains. Complex Anal. Oper. Theory 15, 124 (2021). https://doi.org/10.1007/s11785-021-01178-4

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  • DOI: https://doi.org/10.1007/s11785-021-01178-4

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