The equation of complex Monge-Ampère type and stability of solutions

DOI10.1007/s00208-005-0687-6zbMath1103.32019OpenAlexW2023951423MaRDI QIDQ2491102

Urban Cegrell, Sławomir Kołodziej

Publication date: 26 May 2006

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00208-005-0687-6

zbMATH Keywords

stabilitycapacityplurisubharmonic functionComplex Monge-Ampère operator

Mathematics Subject Classification ID

Plurisubharmonic functions and generalizations (32U05) Currents (32U40)

Related Items (26)

On the regularity of the complex Hessian equation ⋮ Continuity of the complex Monge-Ampère operator on compact Kähler manifolds ⋮ Existence and Hölder continuity to solutions of the complex Monge–Ampère-type equations with measures vanishing on pluripolar subsets ⋮ On the Cegrell classes ⋮ Weak solutions to the complex Monge–Ampère equation on hyperconvex domains ⋮ The complex Monge-Ampère type equation for \(\mathcal{F}\)-plurisubharmonic functions ⋮ Hölder continuity of solutions to the Monge-Ampère equations on compact Kähler manifolds ⋮ Some weighted energy classes of plurisubharmonic functions ⋮ Weak solutions to complex Monge-Ampère equations on compact Kähler manifolds ⋮ Capacity and stability on some Cegrell classes of \(m\)-subharmonic functions ⋮ Continuous solutions for degenerate complex Hessian equation ⋮ Weak solutions to complex Hessian type equations in the class \(\mathcal{E}_{\phi}(X, \omega, m)\) ⋮ Weak solutions to the complex Hessian type equations for arbitrary measures ⋮ Convergence in capacity of plurisubharmonic functions with given boundary values ⋮ Hölder continuity for solutions of the complex Monge-Ampère type equation ⋮ Convergence in capacity ⋮ A Dirichlet problem for the complex Monge-Ampère operator in \(\mathcal F(f)\) ⋮ The stability of solutions to the complex Monge-Ampère equations in bounded \(\mathcal{F} \)-hyperconvex domains ⋮ Measures of finite pluricomplex energy ⋮ Equations of complex Monge–Ampère type for arbitrary measures and applications ⋮ Weak solutions to the complex \(m\)-Hessian type equation on open subsets of \(\mathbb{C}^n\) ⋮ An inequality for mixed Monge-Ampère measures ⋮ On a family of quasimetric spaces in generalized potential theory ⋮ Weak subsolutions to complex Monge-Ampère equations ⋮ Weak solutions to Monge-Ampère type equations on compact Hermitian manifold with boundary ⋮ Weak solutions to the complex \(m\)-Hessian type equations for arbitrary nonnegative Radon measures on open subsets of \(\mathbb{C}^n\)

Cites Work

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• The dirichlet problem for nonlinear second-order elliptic equations. II. Complex monge-ampère, and uniformaly elliptic, equations
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• The range of the complex Monge-Ampere operator II
• On the Dirichlet problem for the complex Monge-Ampère operator
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