Symplectic factorization, Darboux theorem and ellipticity

DOI10.1016/j.anihpc.2017.04.005zbMath1476.58037OpenAlexW2613603952MaRDI QIDQ1697422

Bernard Dacorogna, Wilfrid Gangbo, Olivier Kneuss

Publication date: 20 February 2018

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.anihpc.2017.04.005

zbMATH Keywords

elliptic systemssymplectic decompositionDarboux theorem for symplectic formsoptimal transport of symplectic forms

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Invariance and symmetry properties for PDEs on manifolds (58J70) Second-order elliptic systems (35J47) First-order elliptic systems (35J46)

Related Items (6)

The Pullback Equation ⋮ Transportation of closed differential forms with non-homogeneous convex costs ⋮ On the equation \((Du)^tHDu=G\) ⋮ On the equation \(A \nabla u + \left( \nabla u\right)^t A = G\) ⋮ Optimal transport of closed differential forms for convex costs ⋮ Quasiconvexity and relaxation in optimal transportation of closed differential forms

Cites Work

• The Monge problem for strictly convex norms in \(\mathbb R^d\)
• The pullback equation for differential forms
• On the pullback equation \(\varphi ^*(g)=f\)
• Partial differential equations. 4th ed
• The geometry of optimal transportation
• Formes-volume sur les variétés à bord
• The second order pullback equation
• A nonholonomic Moser theorem and optimal transport
• Constructing optimal maps for Monge’s transport problem as a limit of strictly convex costs
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
• Polar factorization and monotone rearrangement of vector‐valued functions
• Elliptic Partial Differential Equations of Second Order
• Differential equations methods for the Monge-Kantorovich mass transfer problem
• On the Volume Elements on a Manifold
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II
• Polar factorization of maps on Riemannian manifolds
• Optimal transport of closed differential forms for convex costs

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