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Abstract Given a probability space X and a bounded domain in d equipped with the Lebesgue measure normalized so that 1 it is shown under additional technical

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Polar Factorization and Monotone Rearrangement of Vector Valued Functions YANN BRENIER Universite de Paris VI Abstract Given a probability space X p and a bounded domain R in R d

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Through this result the concepts of polar factorization of real matrices Helmholtz decomposition of vector fields and nondecreasing rearrangements of real valued functions are unified The Monge

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directeur de recherches CNRS LMO Universit Paris Saclay Cited by 11 647 Mathematics

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In optimal transport a branch of mathematics polar factorization of vector fields is a basic result due to Brenier 1987 1 with antecedents of Knott Smith 1984 2 and Rachev 1985 3 that

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However Y BREMER Brl Br2 proved that there exists a convex function wh se gradient s equal to u up to a rearrangement provided that u satisfies a nondegeneracy condition the so called N 1 property

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Through this result the concepts of polar factorization of real matrices Helmholtz decomposition of vector fields and nondecreasing rearrangements of real valued functions are unified The

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Polar factorization and monotone rearrangement of vector valued functions DOI Web Site Web Site 14 Citations Yann Brenier

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