We study the Kantorovich-Rubinstein transhipment problem when the difference between the source and the target is not anymore a balanced measure but belongs to a suitable subspace X(Ω) of first order distribution. A particular P subclass X 0 (Ω) of such distributions will be considered which includes the infinite sums of dipoles k (δ p k − δ n k ) studied in [28, 29]. In spite of this weakened regularity, it is shown that an optimal transport density still exists among nonnegative finite measures. Some geometric properties of the Banach spaces X(Ω) and X ♯ 0 (Ω) can be then deduced.

The Monge-Kantorovich problem for distributions and applications / G. BOUCHITTE; BUTTAZZO G; L. DE PASCALE. - In: JOURNAL OF CONVEX ANALYSIS. - ISSN 0944-6532. - STAMPA. - 17:(2010), pp. 925-943.

The Monge-Kantorovich problem for distributions and applications

DE PASCALE, LUIGI
2010

Abstract

We study the Kantorovich-Rubinstein transhipment problem when the difference between the source and the target is not anymore a balanced measure but belongs to a suitable subspace X(Ω) of first order distribution. A particular P subclass X 0 (Ω) of such distributions will be considered which includes the infinite sums of dipoles k (δ p k − δ n k ) studied in [28, 29]. In spite of this weakened regularity, it is shown that an optimal transport density still exists among nonnegative finite measures. Some geometric properties of the Banach spaces X(Ω) and X ♯ 0 (Ω) can be then deduced.
2010
17
925
943
G. BOUCHITTE; BUTTAZZO G; L. DE PASCALE
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1070967
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