On singular Abreu equations in higher dimensions

DOI10.1007/s11854-021-0176-1zbMath1481.35163arXiv1905.09696OpenAlexW4205089897MaRDI QIDQ2073017

Nam Q. Le

Publication date: 27 January 2022

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.09696

zbMATH Keywords

existenceuniquenessDirichlet conditionconvex solutionnonlinear fourth order equation

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Nonlinear elliptic equations (35J60) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (1)

Interior estimates for the Monge-Ampère type fourth order equations

Cites Work

• A note on interior \(W^{2,1+ \varepsilon }\) estimates for the Monge-Ampère equation
• \(W^{2,1+\varepsilon}\) estimates for the Monge-Ampère equation
• The Monge-Ampère equation and its applications
• Approximation of variational problems with a convexity constraint by PDEs of Abreu type
• Global Hölder estimates for 2D linearized Monge-Ampère equations with right-hand side in divergence form
• Boundary regularity for the Monge-Ampère and affine maximal surface equations
• Global \(W^{1,p}\) estimates for solutions to the linearized Monge-Ampère equations
• Global 𝑊^{2,𝑝} estimates for the Monge-Ampère equation
• Elliptic Partial Differential Equations of Second Order
• KÄHLER GEOMETRY OF TORIC VARIETIES AND EXTREMAL METRICS
• Ironing, Sweeping, and Multidimensional Screening
• Pointwise 𝐶^{2,𝛼} estimates at the boundary for the Monge-Ampère equation
• Singular Abreu Equations and Minimizers of Convex Functionals with a Convexity Constraint

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