Equivalence between some definitions for the optimal mass transport problem and for the transport density on manifolds

DOI10.1007/s10231-004-0109-5zbMath1099.49030OpenAlexW2034643926MaRDI QIDQ2505598

Aldo Pratelli

Publication date: 27 September 2006

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10231-004-0109-5

zbMATH Keywords

shape optimizationmass transportationtransport density

Mathematics Subject Classification ID

Deterministic network models in operations research (90B10) Variational problems in a geometric measure-theoretic setting (49Q20) Integration on manifolds; measures on manifolds (58C35) Vector-valued measures and integration (46G10)

Related Items (14)

Computing the cut locus of a Riemannian manifoldviaoptimal transport ⋮ Beckmann-type problem for degenerate Hamilton-Jacobi equations ⋮ Unbalanced and partial \(L_1\) Monge-Kantorovich problem: a scalable parallel first-order method ⋮ Mass Optimization Problem with Convex Cost ⋮ Optimal Transport Approach to Sobolev Regularity of Solutions to the Weighted Least Gradient Problem ⋮ Optimal mass transportation for costs given by Finsler distances via \(p\)-Laplacian approximations ⋮ Remarks on the stability of mass minimizing currents in the Monge-Kantorovich problem ⋮ Optimal partial mass transportation and obstacle Monge-Kantorovich equation ⋮ Comparison between W₂ distance and Ḣ⁻¹ norm, and Localization of Wasserstein distance ⋮ On the sufficiency of \(c\)-cyclical monotonicity for optimality of transport plans ⋮ Monge-Kantorovich equation for degenerate Finsler metrics ⋮ A Mixed Formulation of the Monge-Kantorovich Equations ⋮ Equivalent formulations for Monge-Kantorovich equation ⋮ Continuity of an optimal transport in Monge problem

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