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Hölder continuity for solutions of the complex Hessian type equation

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Abstract

In this paper we prove the Hölder continuity for the Hessian equation on a m-hyperconvex domain of m-subharmonic type k. As an application we prove the existence and investigate the Hölder continuity of solutions to the Dirichlet problem of the complex Hessian type equation on a bounded strictly m-pseudoconvex domain \(\Omega \) in \(\mathbb {C}^{n}\).

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Acknowledgements

The authors would like to thank the referees very much for remarks which led to the improvement of the exposition of the paper.

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Authors and Affiliations

  1. Laboratory LaREAMI, Department of Mathematics, Regional Centre of Trades of Education and Training, Kenitra, Morocco

    Hichame Amal

  2. Department of Mathematics, Faculty of Sciences, Ibn Tofail University, PO 242, Kenitra, Morocco

    Saïd Asserda & Manar Bouhssina

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  1. Hichame Amal
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  2. Saïd Asserda
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  3. Manar Bouhssina
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Correspondence to Manar Bouhssina.

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Amal, H., Asserda, S. & Bouhssina, M. Hölder continuity for solutions of the complex Hessian type equation. Rend. Circ. Mat. Palermo, II. Ser 73, 267–289 (2024). https://doi.org/10.1007/s12215-023-00919-y

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  • DOI: https://doi.org/10.1007/s12215-023-00919-y

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