Complex Hessian-type equations in the weighted m-subharmonic class

Authors

  • Mohamed Zaway Department of Mathematics, Faculty of Sciences of Sfax, University of Sfax, Tunisia and Irescomath Laboratory, Gabes University, Zrig Gabes, Tunisia
  • Jawhar Hbil Department of Mathematics, Jouf University, Sakaka, Saudi Arabia and Irescomath Laboratory, Gabes University, Zrig Gabes, Tunisia

DOI:

https://doi.org/10.37863/umzh.v75i6.7122

Keywords:

m-subharmonic function, Capacity, Hessian operator.

Abstract

UDC 517.5

We study the existence of a solution to a general type of complex Hessian equation on some Cegrell classes. For a given measure μ defined on an m-hyperconvex domain  Ω⊂Cn,  under  suitable conditions, we prove that the equation χ(.)Hm(.)=μ has a solution that belongs to the class Em,χ(Ω).

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Published

20.06.2023

Issue

Vol. 75 No. 6 (2023)

Section

Research articles

How to Cite

Zaway, Mohamed, and Jawhar Hbil. “Complex Hessian-Type Equations in the Weighted m-Subharmonic Class”. Ukrains’kyi Matematychnyi Zhurnal, vol. 75, no. 6, June 2023, pp. 805-16, https://doi.org/10.37863/umzh.v75i6.7122.