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<p>In this paper, we introduce finite energy classes of quaternionic <i>m</i>-plurisubharmonic functions of Cegrell type and define the quaternionic <i>m</i>-Hessian operator on some Cegrell’s classes. We use the variational approach to solve the quaternionic <i>m</i>-Hessian equation when the right-hand side is a positive Radon measure.</p>

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A Variational Approach to the Quaternionic Hessian Equation

  • 期刊论文

  • 发表日期：

    2025年2月21日

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  • Hichame Amal,
  • Saïd Asserda,
  • Mohamed Barloub

摘要

In this paper, we introduce finite energy classes of quaternionic m-plurisubharmonic functions of Cegrell type and define the quaternionic m-Hessian operator on some Cegrell’s classes. We use the variational approach to solve the quaternionic m-Hessian equation when the right-hand side is a positive Radon measure.