Non-existence of polar factorisations and polar inclusion of a vector-valued mapping

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dc.contributor.author Douglas, Robert J.
dc.date.accessioned 2007-12-03T14:39:16Z
dc.date.available 2007-12-03T14:39:16Z
dc.date.issued 2007
dc.identifier.citation Douglas , R J 2007 , ' Non-existence of polar factorisations and polar inclusion of a vector-valued mapping ' International Journal of Pure and Applied Mathematics , vol 41 , no. 3 . en
dc.identifier.other PURE: 73646
dc.identifier.other dspace: 2160/379
dc.identifier.uri http://hdl.handle.net/2160/379
dc.identifier.uri http://math.uctm.edu/journals/index.html en
dc.description R.J. DOUGLAS, Non-existence of polar factorisations and polar inclusion of a vector-valued mapping. Intern. Jour. Of Pure and Appl. Math., (IJPAM) 41, no. 3 (2007). en
dc.description.abstract This paper proves some results concerning the polar factorisation of an integrable vector-valued function $u$ into the composition $u = u^{\#} \circ s$, where $u^{\#} = \nabla \psi$ almost everywhere for some convex function $\psi$, and $s$ is 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 $u(x) \in \partial \psi (y)$ 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. en
dc.language.iso eng
dc.relation.ispartof International Journal of Pure and Applied Mathematics en
dc.title Non-existence of polar factorisations and polar inclusion of a vector-valued mapping en
dc.type Text en
dc.type.publicationtype Article (Journal) en
dc.contributor.institution Institute of Mathematics & Physics (ADT) en
dc.contributor.institution Mathematical Modelling of Structures, Solids and Fluids en
dc.description.status Peer reviewed en


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