Uniqueness of the polar factorisation and projection of a vector-valued mapping

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dc.contributor.author Douglas, Robert J.
dc.contributor.author Burton, G. R.
dc.date.accessioned 2007-12-03T14:47:44Z
dc.date.available 2007-12-03T14:47:44Z
dc.date.issued 2003-05
dc.identifier.citation Douglas , R J & Burton , G R 2003 , ' Uniqueness of the polar factorisation and projection of a vector-valued mapping ' Annales de l'Institut Henri Poincare (C) Non Linear Analysis , vol 20 , no. 3 , pp. 405-418 . en
dc.identifier.issn 0294-1449
dc.identifier.other PURE: 73670
dc.identifier.other dspace: 2160/380
dc.identifier.uri http://hdl.handle.net/2160/380
dc.description G.R. BURTON and R.J. DOUGLAS, Uniqueness of the polar factorisation and projection of a vector-valued mapping. Ann. I.H. Poincare â A.N. 20 (2003), 405-418. 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 $u^{\#}$ is equal almost everywhere to the gradient of a convex function, and $s$ is a measure-preserving mapping. It is shown that the factorisation is unique (i.e. the measure-preserving mapping $s$ is unique) precisely when $u^{\#}$ is almost injective. Not every integrable function has a polar factorisation; we introduce a class of counterexamples. It is further shown that if $u$ is square integrable, then measure-preserving mappings $s$ which satisfy $u = u^{\#} \circ s$ are exactly those, if any, which are closest to $u$ in the $L^2$-norm. en
dc.format.extent 14 en
dc.language.iso eng
dc.relation.ispartof Annales de l'Institut Henri Poincare (C) Non Linear Analysis en
dc.title Uniqueness of the polar factorisation and projection of a vector-valued mapping en
dc.type Text en
dc.type.publicationtype Article (Journal) en
dc.identifier.doi http://dx.doi.org/10.1016/S0294-1449(02)00026-4
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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