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Weak Solutions to the Complex m-Hessian Type Equation on Open Subsets of \({\mathbb {C}}^n\)

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Abstract

In the paper, we prove the existence of weak solutions of the complex m-Hessian type equation on an open subset \(\Omega \) of \({\mathbb {C}}^n\). In the end of the paper, we give a result related to the complex 1-Hessian type equation in the unit ball of \({\mathbb {C}}^2\).

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Acknowledgements

The authors would like to thank the anonymous reviewers very much for suggestions and valuable remarks which led to the improvement of the exposition of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Hanoi National University of Education, Hanoi, Viet Nam

    Le Mau Hai

  2. Hanoi Architectural University, Hanoi, Viet Nam

    Vu Van Quan

Authors
  1. Le Mau Hai
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  2. Vu Van Quan
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Correspondence to Le Mau Hai.

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Communicated by Heinrich Begehr.

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This article is part of the topical collection “Higher Dimensional Geometric Function Theory and Hypercomplex Analysis” edited by Irene Sabadini, Michael Shapiro and Daniele Struppa.

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Hai, L.M., Van Quan, V. Weak Solutions to the Complex m-Hessian Type Equation on Open Subsets of \({\mathbb {C}}^n\). Complex Anal. Oper. Theory 15, 84 (2021). https://doi.org/10.1007/s11785-021-01122-6

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