Optimal transport of closed differential forms for convex costs

Let c : A(k-1) -> R+ be convex and Omega subset of R-n be a bounded domain. Let f(0) and f(1) be two closed k-forms on Omega satisfying appropriate boundary conditions. We discuss the minimization of integral(Omega) c (A) dx over a subset of (k - 1)-forms A on Omega such that dA + f(1) - f(0) = 0, and its connection with a transport of symplectic forms. Section 3 mainly serves as a step toward Section 4, which is richer, as it connects to variational problems with multiple minimizers. (C) 2015 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.


Published in:
Comptes Rendus Mathematique, 353, 12, 1099-1104
Year:
2015
Publisher:
Paris, Elsevier France-Editions Scientifiques Medicales Elsevier
ISSN:
1631-073X
Laboratories:




 Record created 2016-02-16, last modified 2018-01-28


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