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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\((\Omega )\).

Keywords

Plurifinely pluripotential theory Plurifinely plurisubharmonic functions Complex Monge–Ampère equations 

Mathematics Subject Classification

32U05 32U15 

Notes

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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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsHanoi National University of EducationHanoiVietnam
  2. 2.Department of Basis SciencesUniversity of Transport TechnologyHanoiVietnam

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