Interior \(C^{1,\alpha}\) regularity for the linearized Monge-Ampère equation with VMO type coefficients

DOI10.1007/s43036-019-00012-1zbMath1433.35159arXiv1810.04507OpenAlexW3001844411MaRDI QIDQ2289841

Qian Zhang, Lin Tang

Publication date: 27 January 2020

Published in: Advances in Operator Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.04507

zbMATH Keywords

linearized Monge-Ampère equation\(C^{1, \alpha}\) estimatesVMO-type condition

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) A priori estimates in context of PDEs (35B45) Monge-Ampère equations (35J96)

Cites Work

• Some minimization problems in the class of convex functions with prescribed determinant
• Interior gradient estimates for solutions to the linearized Monge-Ampère equation
• A localization property of viscosity solutions to the Monge-Ampère equation and their strict convexity
• The Bernstein problem for affine maximal hypersurfaces
• Global \(W^{2,p}\) regularity on the linearized Monge-Ampère equation with \(\text{VMO}\) Type coefficients
• \(W^{4, p}\) solution to the second boundary value problem of the prescribed affine mean curvature and Abreu's equations
• Properties of the solutions of the linearized Monge-Ampere equation
• 𝑊^{{}2,𝑝}–estimates for the linearized Monge–Ampère equation
• A Fully Nonlinear Version of the Incompressible Euler Equations: The Semigeostrophic System
• Sharp regularity results on second derivatives of solutions to the Monge-Ampère equation with VMO type data
• Polar factorization and monotone rearrangement of vector‐valued functions
• Some regularity properties of solutions of Monge Ampère equation
• Interior second derivative estimates for solutions to the linearized Monge-Ampère equation
• The Monge-Ampère equation

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