The Guillemin boundary problem for Monge-Ampère equation in the polygon

DOI10.1016/j.aim.2023.108885OpenAlexW4318774592MaRDI QIDQ2684532

Genggeng Huang

Publication date: 16 February 2023

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2023.108885

zbMATH Keywords

existenceMonge-Ampère equationGuillemin boundary condition

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Monge-Ampère equations (35J96)

Cites Work

• The Monge-Ampère equation with Guillemin boundary conditions
• Schauder estimates for degenerate Monge-Ampère equations and smoothness of the eigenfunctions
• Extremal metrics on toric surfaces: a continuity method
• Constant scalar curvature metrics on toric surfaces
• Kaehler structures on toric varieties
• Scalar curvature and stability of toric varieties.
• A localization theorem and boundary regularity for a class of degenerate Monge-Ampere equations
• Interior estimates for the \(n\)-dimensional Abreu's equation
• Interior estimates for solutions of Abreu equation
• Existence of Global Smooth Solutions to Dirichlet Problem for Degenerate Elliptic Monge–Ampere Equations
• KÄHLER GEOMETRY OF TORIC VARIETIES AND EXTREMAL METRICS
• Boundary regularity for Monge-Ampère equations with unbounded right hand side
• On the constant scalar curvature Kähler metrics (I)—A priori estimates
• On the constant scalar curvature Kähler metrics (II)—Existence results

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