Complex Hessian-type equations in the weighted $m$-subharmonic class
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 $\mu$ defined on an $m$-hyperconvex domain  $\Omega \subset \mathbb{C}^n,$  under  suitable condi...
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| Date: | 2023 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2023
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/7122 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | 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 $\mu$ defined on an $m$-hyperconvex domain  $\Omega \subset \mathbb{C}^n,$  under  suitable conditions, we prove that the equation $\chi(.) H_m(.)=\mu$ has a solution that belongs to the class $\mathcal{E}_{m,\chi}(\Omega).$ |
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| DOI: | 10.37863/umzh.v75i6.7122 |