Complex Hessian-type equations in the weighted \(m\)-subharmonic class

DOI10.1007/s11253-023-02237-zOpenAlexW4388571208MaRDI QIDQ6147986

Mohamed Zaway, Jawhar Hbil

Publication date: 11 January 2024

Published in: Ukrainian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11253-023-02237-z

zbMATH Keywords

\(m\)-subharmonic functionscomplex Hessian equationCegrell class

Mathematics Subject Classification ID

Plurisubharmonic functions and generalizations (32U05) Other partial differential equations of complex analysis in several variables (32W50)

Cites Work

• Local property of a class of \(m\)-subharmonic functions
• Potential theory in the class of \(m\)-subharmonic functions
• Pluricomplex energy
• The general definition of the complex Monge-Ampère operator.
• Weak solutions to the complex Hessian type equations for arbitrary measures
• Weak solutions to the complex \(m\)-Hessian equation on open subsets of \(\mathbb{C}^n\)
• A variational approach to complex Hessian equations in \(\mathbb{C}^n\)
• Maximal \(m\)-subharmonic functions and the Cegrell class \(\mathcal{N}_m\)
• Weak solutions to the complex Hessian equation.
• The Monge–Ampère type equation in the weighted pluricomplex energy class
• On a Monge–Ampère type equation in the Cegrell class E_χ
• Plurisubharmonic functions with weak singularities
• The Dirichlet problem for the complex Hessian operator in the class $\mathcal{N}_m(\Omega,f)$
• Hessian measures on m-polar sets and applications to the complex Hessian equations
• Capacity and stability on some Cegrell classes of \(m\)-subharmonic functions