The Dirichlet problem for the complex Hessian operator in the class $\mathcal{N}_m(\Omega,f)$


  • Ayoub El Gasmi



Let $\Omega\subset \mathbb{C}^{n}$ be a bounded $m$-hyperconvex domain, where $m$ is an integer such that $1\leq m\leq n$. Let $\mu$ be a positive Borel measure on $\Omega$. We show that if the complex Hessian equation $H_m (u) = \mu$ admits a (weak) subsolution in $\Omega$, then it admits a (weak) solution with a prescribed least maximal $m$-subharmonic majorant in $\Omega$.


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How to Cite

El Gasmi, A. (2021). The Dirichlet problem for the complex Hessian operator in the class $\mathcal{N}_m(\Omega,f)$. MATHEMATICA SCANDINAVICA, 127(2), 287–316.