# The Monge-Kantorovich problem for distributions and applications

arXiv: https://arxiv.org/abs/1312.5453 · HTML: https://mlsanity.com/paper/1312.5453/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Dec 2013.

## Built on by (most cited first, 1 of 1)

- [A Survey on Algorithmic Developments in Optimal Transport Problem with Applications](https://mlsanity.com/paper/2501.06247/) (2025)

## Abstract (arXiv)

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(Omega) of first order distribution. A particular subclass X0^sharp(Omega) of such distributions will be considered which includes the infinite sums of dipoles sumk(δpk-δnk) studied in citeP1, P2. 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(Omega) and X0^sharp(Omega) can be then deduced.