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.File | Dimensione | Formato | |
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