Interior $C^2$ estimate for Monge-Ampère equation in dimension two

DOI10.1090/proc/15459zbMath1475.35171arXiv2007.11297OpenAlexW3119042712MaRDI QIDQ4985382

Jiakun Liu

Publication date: 23 April 2021

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

Full work available at URL: https://arxiv.org/abs/2007.11297

zbMATH Keywords

interior estimateMonge-Ampère equationpartial Legendre transform

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Monge-Ampère equations (35J96)

Related Items (2)

Solvability of a class of singular fourth order equations of Monge-Ampère type ⋮ Interior estimates for the Monge-Ampère type fourth order equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The interior \(C^2\) estimate for the Monge-Ampère equation in dimension \(n = 2\)
• The Monge-Ampère equation and its applications
• On certain nonlinear elliptic differential equations and univalent mappings
• On Pogorelov estimates for Monge-Ampère type equations
• Regularity theory for quasilinear elliptic systems and Monge-Ampère equations in two dimensions
• Regularity of a class of quasilinear degenerate elliptic equations
• Two-dimensional Monge-Ampère equations under incomplete Hölder assumptions
• On elliptic Monge-Ampère equations and Weyl's embedding problem
• Schauder estimates for elliptic and parabolic equations
• Partial Legendre transforms of non-linear equations
• Special Lagrangian Equations
• On Monge-Ampère equations with homogenous right-hand sides
• Elliptic Partial Differential Equations of Second Order
• The Weyl and Minkowski problems in differential geometry in the large

This page was built for publication: Interior $C^2$ estimate for Monge-Ampère equation in dimension two