Non-existence of polar factorisations and polar inclusion of a vector-valued mapping
| dc.creator | Douglas, R. J. | |
| dc.date | 2007-12-13 | |
| dc.date.accessioned | 2026-07-07T08:49:01Z | |
| dc.date.available | 2026-07-07T08:49:01Z | |
| dc.description | This paper proves some results concerning the polar factorisation of an integrable vector-valued function u into the composition of the gradient of a convex function with a measure-preserving mapping. Not every integrable function has a polar factorisation; we extend the class of counterexamples. We introduce a generalisation: u has a polar inclusion if u(x) belongs to the subdifferential of the convex function at y for almost every pair (x,y) with respect to a measure-preserving plan. Given a regularity assumption, we show that such measure-preserving plans are exactly the minimisers of a Monge-Kantorovich optimisation problem. | |
| dc.description | 9 pages, 0 figures, to be published in the International Journal of Pure and Applied Mathematics, IJPAM, 41, no. 3, 2007, 363-374 | |
| dc.identifier | https://arxiv.org/abs/0712.2161 | |
| dc.identifier | http://arxiv.org/abs/0712.2161 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144154 | |
| dc.subject | Functional Analysis | |
| dc.subject | 28D05 (Primary); 28A50, 46E30 (Secondary) | |
| dc.title | Non-existence of polar factorisations and polar inclusion of a vector-valued mapping | |
| dc.type | text |