Approximation of \(m\)-subharmonic function with given boundary values

DOI10.1016/J.JMAA.2024.128097MaRDI QIDQ6198313

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Publication date: 21 February 2024

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

\(m\)-subharmonic functions\(m\)-Hessian operator\(m\)-hyperconvex domainssubextension of \(m\)-subharmonic functionsapproximation of \(m\)-subharmonic functions

Mathematics Subject Classification ID

Pluripotential theory (32Uxx) Generalizations of potential theory (31Cxx) Differential operators in several variables (32Wxx)

Cites Work

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• Potential theory in the class of \(m\)-subharmonic functions
• A new capacity for plurisubharmonic functions
• Subextension and approximation of negative plurisubharmonic functions
• Pluricomplex energy
• Subextension of plurisubharmonic functions with bounded Monge--Ampère mass
• The geometry of \(m\)-hyperconvex domains
• On the weighted \(m\)-energy classes
• 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.
• APPROXIMATION OF NEGATIVE PLURISUBHARMONIC FUNCTIONS WITH GIVEN BOUNDARY VALUES
• A comparison principle for the complex Monge-Ampère operator in Cegrell’s classes and applications
• 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

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