Solution of the Dirichlet problem for the prescribed Jacobian equation using the Monge-Ampère equation

DOI10.1016/j.crma.2012.04.005zbMath1243.35038OpenAlexW1997148491MaRDI QIDQ424745

Guillaume Carlier, Bernard Dacorogna

Publication date: 4 June 2012

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2012.04.005

zbMATH Keywords

solvabilityoptimal regularity

Mathematics Subject Classification ID

Boundary value problems for nonlinear first-order PDEs (35F30)

Related Items (6)

The Pullback Equation ⋮ The Dirichlet problem for the Jacobian equation in critical and supercritical Sobolev spaces ⋮ A least-squares method for the solution of the non-smooth prescribed Jacobian equation ⋮ Nonlinear open mapping principles, with applications to the Jacobian equation and other scale-invariant PDEs ⋮ Bi-Sobolev solutions to the prescribed Jacobian inequality in the plane with \(L^{p}\) data and applications to nonlinear elasticity ⋮ An Alternating Direction Method of Multipliers for the Numerical Solution of a Fully Nonlinear Partial Differential Equation Involving the Jacobian Determinant

Cites Work

• The pullback equation for differential forms
• Boundary regularity of maps with convex potentials. II
• On manifolds homeomorphic to the 7-sphere
• On a partial differential equation involving the Jacobian determinant
• On the regularity of the polar factorization for time dependent maps
• Polar factorization and monotone rearrangement of vector‐valued functions
• Elliptic Partial Differential Equations of Second Order
• On the second boundary value problem for equations of Monge-Ampère type.
• Shape recognition via Wasserstein distance

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