On the regularity of the polar factorization for time dependent maps

DOI10.1007/s00526-004-0280-yzbMath1116.35033arXivmath/0306431OpenAlexW2040462165MaRDI QIDQ2575178

Grégoire Loeper

Publication date: 8 December 2005

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0306431

zbMATH Keywords

Monge-Ampère equationpolar factorizationtime dependent maps

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear parabolic equations (35K55) Nonlinear elliptic equations (35J60) Regularity of solutions in optimal control (49N60)

Related Items (13)

Hölder regularity of the 2D dual semigeostrophic equations via analysis of linearized Monge-Ampère equations ⋮ On certain degenerate and singular elliptic PDEs. III: Nondivergence form operators and \(RH_\infty\)-weights ⋮ A global existence result for the semigeostrophic equations in three dimensional convex domains ⋮ On certain degenerate and singular elliptic PDEs I: nondivergence form operators with unbounded drifts and applications to subelliptic equations ⋮ Interior estimates for the Monge-Ampère type fourth order equations ⋮ Solution of the Dirichlet problem for the prescribed Jacobian equation using the Monge-Ampère equation ⋮ Convergence rates for discretized Monge-Ampère equations and quantitative stability of optimal transport ⋮ On Hölder continuity-in-time of the optimal transport map towards measures along a curve ⋮ Existence of Eulerian Solutions to the Semigeostrophic Equations in Physical Space: The 2-Dimensional Periodic Case ⋮ Sobolev regularity for the Monge-Ampère equation, with application to the semigeostrophic equations ⋮ Global Hölder estimates for 2D linearized Monge-Ampère equations with right-hand side in divergence form ⋮ Poincaré and Sobolev inequalities in the Monge-Ampère quasi-metric structure ⋮ Constructing a relativistic heat flow by transport time steps

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