𝑊^{{}2,𝑝}–estimates for the linearized Monge–Ampère equation

DOI10.1090/S0002-9947-06-04189-4zbMath1210.35026MaRDI QIDQ3420346

Cristian E. Gutiérrez, Federico Tournier

Publication date: 1 February 2007

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

zbMATH Keywords

viscosity solutionsnonuniformly elliptic equationsa priori estimates of second derivativescross sections of solutions

Mathematics Subject Classification ID

A priori estimates in context of PDEs (35B45) Viscosity solutions to PDEs (35D40) Monge-Ampère equations (35J96)

Related Items (8)

Global \(W^{2,p}\) regularity on the linearized Monge-Ampère equation with \(\text{VMO}\) Type coefficients ⋮ Harnack inequality for the fractional nonlocal linearized Monge-Ampère equation ⋮ Regularity results on the parabolic Monge-Ampère equation with \(VMO\) type data ⋮ Interior gradient estimates for solutions to the linearized Monge-Ampère equation ⋮ Global \(W^{2,p}\) estimates for solutions to the linearized Monge-Ampère equations ⋮ Interior \(C^{1,\alpha}\) regularity for the linearized Monge-Ampère equation with VMO type coefficients ⋮ Sharp regularity results on second derivatives of solutions to the Monge-Ampère equation with VMO type data ⋮ Interior second derivative estimates for solutions to the linearized Monge-Ampère equation

Cites Work

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• Interior \(W^{2,p}\) estimates for solutions of the 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
• Properties of the solutions of the linearized Monge-Ampere equation
• Some Estimates for Nondivergence Structure, Second Order Elliptic Equations
• Second Derivative L p -Estimates for Elliptic Equations of Nondivergent Type
• Some regularity properties of solutions of Monge Ampère equation
• Some Counterexamples to the Regularity of Monge-Ampere Equations
• Geometric properties of the sections of solutions to the Monge-Ampère equation
• Real analysis related to the Monge-Ampère equation
• The Monge-Ampère equation

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