Partial Legendre transforms of non-linear equations

DOI10.1090/S0002-9939-2012-11210-9zbMath1307.35010arXiv1010.2111WikidataQ61645883 ScholiaQ61645883MaRDI QIDQ2846738

Pengfei Guan, Duong H. Phong

Publication date: 3 September 2013

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.2111

zbMATH Keywords

degenerate Monge-Ampère equation

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Transform methods (e.g., integral transforms) applied to PDEs (35A22) Monge-Ampère equations (35J96)

Related Items

Solvability of a class of singular fourth order equations of Monge-Ampère type ⋮ Evans-Krylov estimates for a nonconvex Monge-Ampère equation ⋮ Interior estimates for the Monge-Ampère type fourth order equations ⋮ Interior $C^2$ estimate for Monge-Ampère equation in dimension two

Cites Work

• Unnamed Item
• Unnamed Item
• A maximum rank problem for degenerate elliptic fully nonlinear equations
• A higher-dimensional partial Legendre transform, and regularity of degenerate Monge-Ampère equations
• The Dirichlet problem for degenerate complex Monge-Ampère equations
• A structural condition for microscopic convexity principle
• Geometry of Kähler metrics and foliations by holomorphic discs
• The Dirichlet problem for Hessian equations on Riemannian manifolds
• Regularity of a class of quasilinear degenerate elliptic equations
• On modified Mabuchi functional and Mabuchi moduli space of Kähler metrics on toric bundles
• The space of Kähler metrics.
• A microscopic convexity principle for nonlinear partial differential equations
• Regularity of subelliptic Monge-Ampère equations
• Test configurations for \(k\)-stability and geodesic rays
• The Monge-Ampère operator and geodesics in the space of Kähler potentials
• Space of Kähler Metrics (V) – Kähler Quantization
• Nahm's equations and free-boundary problems
• The Space of Volume Forms
• The dirichlet problem for nonlinear second-order elliptic equations I. Monge-ampégre equation
• Spatiotemporal complexity of the cubic-quintic nonlinear Schrodinger equation