English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper we analyze a mass transportation problem in a bounded domain in which there is the possibility of import/export mass across the boundary paying a tax in addition to the transport cost that is assumed to be given by the Euclidean distance. We show a general duality argument and for the dual problem we nd a Kantorovich poten- tial as the limit as p ! 1 of solutions to p-Laplacian type problems with nonlinear boundary conditions. In addition, we show that this limit en- codes all the relevant information for our problem. It provides the masses that are exported and imported from the boundary and also allows the construction of an optimal transport plan. Finally we show that the ar- guments can be adapted to deal with the case in which the mass that can be exported/imported is bounded by prescribed functions.

An optimal transportation problem with a cost given by the Euclidean distance plus import/export taxes on the boundary