Complex $m$-Hessian type equations in weighted energy classes of $m$-subharmonic functions with given boundary value
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917749054242816 |
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| author | Van Phu, Nguyen Dieu, Nguyen Quang |
| author_facet | Van Phu, Nguyen Dieu, Nguyen Quang |
| contents | In this paper, we concern with the existence of solutions of the complex $m-$Hessian type equation $-χ(u)H_{m}(u)=μ$ in the class $\mathcal{E}_{m,χ}(f,Ω)$ if there exists subsolution in this class, where the given boundary value $f\in\mathcal{N}_m(Ω)\cap MSH_m(Ω).$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_07528 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Complex $m$-Hessian type equations in weighted energy classes of $m$-subharmonic functions with given boundary value Van Phu, Nguyen Dieu, Nguyen Quang Analysis of PDEs Complex Variables 32U05, 32W20 In this paper, we concern with the existence of solutions of the complex $m-$Hessian type equation $-χ(u)H_{m}(u)=μ$ in the class $\mathcal{E}_{m,χ}(f,Ω)$ if there exists subsolution in this class, where the given boundary value $f\in\mathcal{N}_m(Ω)\cap MSH_m(Ω).$ |
| title | Complex $m$-Hessian type equations in weighted energy classes of $m$-subharmonic functions with given boundary value |
| topic | Analysis of PDEs Complex Variables 32U05, 32W20 |
| url | https://arxiv.org/abs/2408.07528 |