The eigenvalue problem for the complex Monge-Ampère operator

DOI10.1007/s12220-023-01407-6zbMath1530.32017arXiv2306.03285OpenAlexW4387043517MaRDI QIDQ6057164

Papa Badiane, Ahmed Zeriahi

Publication date: 25 October 2023

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2306.03285

zbMATH Keywords

Dirichlet problemenergy functionaleigenvalue problemsubsolutionplurisubharmonic functioncomplex Monge-Ampère operator

Mathematics Subject Classification ID

Complex Monge-Ampère operators (32W20) Plurisubharmonic functions and generalizations (32U05)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A variational approach to complex Monge-Ampère equations
• Degenerate complex Monge-Ampère equations
• Maximal subextensions of plurisubharmonic functions
• A new capacity for plurisubharmonic functions
• A gradient estimate in the Calabi-Yau theorem
• An inequality for mixed Monge-Ampère measures
• Two remarks on Monge-Ampère equations
• An eigenvalue problem for the complex Monge-Ampère operator in pseudoconvex domains
• The Dirichlet problem for a complex Monge-Ampère equation
• Méthodes de contrôle optimal en analyse complexe. I: Résolution d'équation de Monge Ampère
• Pluricomplex energy
• The Dirichlet problem for complex Monge-Ampère equations and regularity of the pluri-complex Green function
• On variational principles for the generalized principal eigenvalue of second order elliptic operators and some applications
• Subextension of plurisubharmonic functions with weak singularities
• Equicontinuity of families of plurisubharmonic functions with bounds on their Monge-Ampère masses
• On the \(C^{2,\alpha}\)-regularity of the complex Monge-Ampère equation
• A variational approach to complex Hessian equations in \(\mathbb{C}^n\)
• Complex Monge-Ampère equations and totally real submanifolds
• On a real Monge-Ampère functional
• On Dirichlet's principle and problem
• Some sufficient conditions for solvability of the Dirichlet problem for the complex Monge-Ampère operator
• The dirichlet problem for nonlinear second-order elliptic equations I. Monge-ampégre equation
• The dirichlet problem for nonlinear second-order elliptic equations. II. Complex monge-ampère, and uniformaly elliptic, equations
• Elliptic Partial Differential Equations of Second Order
• The principal eigenvalue and maximum principle for second‐order elliptic operators in general domains
• The $\mathcal C^{2,\alpha}$ estimate of complex Monge-Ampere equation
• Hölder regularity for solutions to complex Monge–Ampère equations
• Hölder continuous solutions to Monge-Ampère equations