Subsolution theorem in weighted energy classes of $m$-subharmonic functions with given boundary value
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909738466279424 |
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| author | Van Phu, Nguyen |
| author_facet | Van Phu, Nguyen |
| contents | In this paper, we concern with the existence of solutions of the weighted complex $m$-Hessian 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 $f\in\mathcal{E}_m(Ω)\cap MSH_m(\Om).$ This is a generalization of the result in the paper \cite{PDtaiwan} where we proved that the subsolution theorem is true in the class $\mathcal{E}_{m,χ}(f,Ω)$ in the case when the given boundary value $f\in\mathcal{N}_m(Ω)\cap MSH_m(\Om).$ |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_11821 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Subsolution theorem in weighted energy classes of $m$-subharmonic functions with given boundary value Van Phu, Nguyen Analysis of PDEs Complex Variables 32U05, 32W20 In this paper, we concern with the existence of solutions of the weighted complex $m$-Hessian 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 $f\in\mathcal{E}_m(Ω)\cap MSH_m(\Om).$ This is a generalization of the result in the paper \cite{PDtaiwan} where we proved that the subsolution theorem is true in the class $\mathcal{E}_{m,χ}(f,Ω)$ in the case when the given boundary value $f\in\mathcal{N}_m(Ω)\cap MSH_m(\Om).$ |
| title | Subsolution theorem 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/2508.11821 |