Subsolution theorem in weighted energy classes of $m$-subharmonic functions with given boundary value

Nguyen Van Phu

Subsolution theorem in weighted energy classes of $m$-subharmonic functions with given boundary value

Analysis of PDEs 2025-08-19 v1 Complex Variables

Authors: Nguyen Van Phu

Abstract

In this paper, we concern with the existence of solutions of the weighted complex $m$ -Hessian 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 $f\in\mathcal{E}_m(\Omega)\cap MSH_m(\Om).$ This is a generalization of the result in the paper \cite{PDtaiwan} where we proved that the subsolution theorem is true in the class $\mathcal{E}_{m,\chi}(f,\Omega)$ in the case when the given boundary value $f\in\mathcal{N}_m(\Omega)\cap MSH_m(\Om).$

Keywords

subsolution theorem weighted energy classes m-subharmonic functions boundary value complex Hessian equation

Cite

@article{arxiv.2508.11821,
  title  = {Subsolution theorem in weighted energy classes of $m$-subharmonic functions with given boundary value},
  author = {Nguyen Van Phu},
  journal= {arXiv preprint arXiv:2508.11821},
  year   = {2025}
}

Comments

11 pages

Subsolution theorem in weighted energy classes of $m$-subharmonic functions with given boundary value

Abstract

Keywords

Cite

Comments

Related papers