Pratelli A (2005)
Publication Language: English
Publication Status: Published
Publication Type: Journal article
Publication year: 2005
Publisher: Springer Verlag (Germany)
Book Volume: 184
Pages Range: 215-238
Journal Issue: 2
DOI: 10.1007/s10231-004-0109-5
In this paper we consider three problems, which are related to the classical Monge's optimal mass transport problem and which are known to be equivalent when the ambient space is an open, convex and bounded subset of R-n; to these problems there correspond different definitions of particular measures (often called transport densities), which are also known to be equivalent. Here We will generalize the setting of these problems and the resulting definitions of transport densities to the case of a Riemannian manifold endowed with a finslerian semidistance, and we will see that the equivalences still hold.
APA:
Pratelli, A. (2005). Equivalence between some definitions for the optimal mass transport problem and for the transport density on manifolds. Annali Di Matematica Pura Ed Applicata, 184(2), 215-238. https://dx.doi.org/10.1007/s10231-004-0109-5
MLA:
Pratelli, Aldo. "Equivalence between some definitions for the optimal mass transport problem and for the transport density on manifolds." Annali Di Matematica Pura Ed Applicata 184.2 (2005): 215-238.
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