The Monge–Ampère type equation in the weighted pluricomplex energy class

DOI10.1142/S0129167X14500426zbMath1301.32023OpenAlexW2070511061MaRDI QIDQ2874717

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Publication date: 8 August 2014

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0129167x14500426

zbMATH Keywords

plurisubharmonic functioncomplex Monge-Ampère operatorenergy classes

Mathematics Subject Classification ID

Complex Monge-Ampère operators (32W20) Plurisubharmonic functions and generalizations (32U05) General pluripotential theory (32U15)

Related Items (11)

Weighted pluricomplex energy. II. ⋮ Existence and Hölder continuity to solutions of the complex Monge–Ampère-type equations with measures vanishing on pluripolar subsets ⋮ Complex Hessian-type equations in the weighted \(m\)-subharmonic class ⋮ Complex Monge-Ampère equations for plurifinely plurisubharmonic functions ⋮ Convergence in capacity of plurisubharmonic functions with given boundary values ⋮ Weighted energy classes of plurifinely plurisubharmonic functions ⋮ Equations of complex Monge–Ampère type for arbitrary measures and applications ⋮ Weak solutions to the complex \(m\)-Hessian type equation on open subsets of \(\mathbb{C}^n\) ⋮ Weakly solutions to the complex Monge-Ampère equation on bounded plurifinely hyperconvex domains ⋮ Envelope of plurisubharmonic functions in Cegrell's classes ⋮ Weak solutions to the complex \(m\)-Hessian type equations for arbitrary nonnegative Radon measures on open subsets of \(\mathbb{C}^n\)

Cites Work

• Some weighted energy classes of plurisubharmonic functions
• Monge-Ampère measures on pluripolar sets
• Mesures de Monge-Ampère et mesures pluriharmoniques. (Monge-Ampère measures and pluriharmonic measures)
• The Dirichlet problem for a complex Monge-Ampère equation
• Pluricomplex energy
• On the definition of the Monge-Ampère operator in \(\mathbb{C}^2\)
• The general definition of the complex Monge-Ampère operator.
• Weighted pluricomplex energy
• Convergence in Capacity
• On a Monge–Ampère type equation in the Cegrell class E_χ
• APPROXIMATION OF WEAKLY SINGULAR PLURISUBHARMONIC FUNCTIONS
• A comparison principle for the complex Monge-Ampère operator in Cegrell’s classes and applications
• A Monge-Ampère norm for delta-plurisubharmonic functions
• Pluripolar sets and the subextension in Cegrell's classes
• A general Dirichlet problem for the complex Monge–Ampère operator
• Continuity of the complex Monge-Ampère operator
• The range of the complex Monge-Ampere operator II
• The domain of definition of the complex Monge-Ampere operator
• Convergence in capacity and applications

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