Complex $m$-Hessian type equations in weighted energy classes of $m$-subharmonic functions with given boundary value

Nguyen Van Phu; Nguyen Quang Dieu

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arXiv · 2408.07528

Complex $m$-Hessian type equations in weighted energy classes of $m$-subharmonic functions with given boundary value

Nguyen Van Phu·Nguyen Quang Dieu

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Abstract

In this paper, we concern with the existence of solutions of the complex $m-$Hessian type equation $-\chi(u)H_{m}(u)=\mu$ in the class $\mathcal{E}_{m,\chi}(f,\Omega)$ if there exists subsolution in this class, where the given boundary value $f\in\mathcal{N}_m(\Omega)\cap MSH_m(\Omega).$

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Nguyen Van Phu, Nguyen Quang Dieu. 2024-08-14. Complex $m$-Hessian type equations in weighted energy classes of $m$-subharmonic functions with given boundary value. https://arxiv.org/abs/2408.07528

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