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Weakly Solutions to the Complex Monge–Ampère Equation on Bounded Plurifinely Hyperconvex Domains

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Abstract

Let \(\mu \) be a non-negative measure defined on bounded \({\mathcal {F}}\)-hyperconvex domain \(\Omega \). We are interested in giving sufficient conditions on \(\mu \) such that we can find a plurifinely plurisubharmonic function satisfying NP\((dd^c u)^n =\mu \) in QB\((\Omega )\).

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Acknowledgements

This article has been partially completed during a stay of the first author at the Vietnam Institute for Advanced Study in Mathematics. He wishes to thank the institution for their kind hospitality and support. This research is funded by the Vietnam Ministry of Education and Training under Grant Number B2018-SPH-57. The authors would like to thank the referees for valuable remarks which led to the improvements of the exposition of the paper.

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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, University of Transport Technology, 54 Trieu Khuc, Thanh Xuan District, Hanoi, Vietnam

    Hoang Van Can

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  1. Nguyen Xuan Hong
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  2. Hoang Van Can
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Correspondence to Nguyen Xuan Hong.

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Communicated by Daniel Aron Alpay.

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Hong, N.X., Van Can, H. Weakly Solutions to the Complex Monge–Ampère Equation on Bounded Plurifinely Hyperconvex Domains. Complex Anal. Oper. Theory 13, 1713–1727 (2019). https://doi.org/10.1007/s11785-018-0821-6

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  • DOI: https://doi.org/10.1007/s11785-018-0821-6

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