Search results for "Mass transportation"

showing 6 items of 6 documents

Optimal mass transportation for costs given by Finsler distances via p-Laplacian approximations

2016

Abstract In this paper we approximate a Kantorovich potential and a transport density for the mass transport problem of two measures (with the transport cost given by a Finsler distance), by taking limits, as p goes to infinity, to a family of variational problems of p-Laplacian type. We characterize the Euler–Lagrange equation associated to the variational Kantorovich problem. We also obtain different characterizations of the Kantorovich potentials and a Benamou–Brenier formula for the transport problem.

010101 applied mathematicsMass transportApplied Mathematics010102 general mathematicsp-LaplacianApplied mathematics0101 mathematicsMass transportation01 natural sciencesAnalysisMathematicsAdvances in Calculus of Variations
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Optimal transport maps on Alexandrov spaces revisited

2018

We give an alternative proof for the fact that in $n$-dimensional Alexandrov spaces with curvature bounded below there exists a unique optimal transport plan from any purely $(n-1)$-unrectifiable starting measure, and that this plan is induced by an optimal map.

Mathematics - Differential GeometryClass (set theory)Pure mathematicsGeneral MathematicsExistential quantificationPlan (drawing)Algebraic geometryoptimaalisuusCurvatureMeasure (mathematics)Primary 53C23. Secondary 49K30Mathematics - Analysis of PDEsMathematics - Metric GeometryFOS: Mathematicsmass transportationMathematics::Metric GeometryMathematicsAlexandrov-avaruudetMetric Geometry (math.MG)Number theoryDifferential Geometry (math.DG)Bounded functionMathematics::Differential GeometrymassasiirtoAlexandrov spacesAnalysis of PDEs (math.AP)
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Mass transportation on sub-Riemannian structures of rank two in dimension four

2017

International audience; This paper is concerned with the study of the Monge optimal transport problem in sub-Riemannian manifolds where the cost is given by the square of the sub-Riemannian distance. Our aim is to extend previous results on existence and uniqueness of optimal transport maps to cases of sub-Riemannian structures which admit many singular minimizing geodesics. We treat here the case of sub-Riemannian structures of rank two in dimension four.

Mathematics - Differential Geometry[ MATH ] Mathematics [math]Rank (linear algebra)Geodesicpolar factorization[MATH] Mathematics [math]01 natural sciencesSquare (algebra)CombinatoricsDimension (vector space)0103 physical sciencesFOS: MathematicsUniqueness0101 mathematicsMass transportation[MATH]Mathematics [math]Mathematical PhysicsComputingMilieux_MISCELLANEOUSMathematicsApplied Mathematics010102 general mathematicsSub-Riemannian geometryDifferential Geometry (math.DG)[MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG]010307 mathematical physicsMathematics::Differential GeometryAnalysisOptimal transport problem
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Finite speed of propagation in porous media by mass transportation methods

2004

Abstract In this Note we make use of mass transportation techniques to give a simple proof of the finite speed of propagation of the solution to the one-dimensional porous medium equation. The result follows by showing that the difference of support of any two solutions corresponding to different compactly supported initial data is a bounded in time function of a suitable Monge–Kantorovich related metric. To cite this article: J.A. Carrillo et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).

Partial differential equationTime functionMass transferBounded functionMathematical analysisMetric (mathematics)GeometryGeneral MedicineMass transportationPorous mediumMathematicsComptes Rendus Mathematique
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L∞ estimates in optimal mass transportation

2016

We show that in any complete metric space the probability measures μ with compact and connected support are the ones having the property that the optimal transportation distance to any other probability measure ν living on the support of μ is bounded below by a positive function of the L∞ transportation distance between μ and ν. The function giving the lower bound depends only on the lower bound of the μ-measures of balls centered at the support of μ and on the cost function used in the optimal transport. We obtain an essentially sharp form of this function. In the case of strictly convex cost functions we show that a similar estimate holds on the level of optimal transport plans if and onl…

Sequence010102 general mathematicsta111Function (mathematics)01 natural sciencesUpper and lower boundsComplete metric space010101 applied mathematicsCombinatoricsMetric spaceBounded functionoptimal mass transportationWasserstein distance0101 mathematicsConvex functionAnalysisProbability measureMathematicsJournal of Functional Analysis
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Existence of optimal transport maps in very strict CD(K,∞) -spaces

2018

We introduce a more restrictive version of the strict CD(K,∞) -condition, the so-called very strict CD(K,∞) -condition, and show the existence of optimal maps in very strict CD(K,∞) -spaces despite the possible lack of uniqueness of optimal plans. peerReviewed

metric measure spacesdifferentiaaligeometriaRicci curvatureoptimal mass transportationvariaatiolaskentaexistence of optimal mapsmittateoriametriset avaruudetbranching geodesics
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