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Invariant K-minimal Sets in the Discrete and Continuous SettingsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2017 (English)In: Journal of Fourier Analysis and Applications, ISSN 1069-5869, E-ISSN 1531-5851, Vol. 23, no 3, 572-611 p.Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Springer, 2017. Vol. 23, no 3, 572-611 p.
##### Keyword [en]

Invariant K-minimal sets, Taut strings, Real interpolation
##### National Category

Mathematical Analysis
##### Identifiers

URN: urn:nbn:se:liu:diva-132425DOI: 10.1007/s00041-016-9479-5ISI: 000401411900003OAI: oai:DiVA.org:liu-132425DiVA: diva2:1045672
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Available from: 2016-11-10 Created: 2016-11-10 Last updated: 2017-06-13Bibliographically approved
##### In thesis

A sufficient condition for a set Ω ⊂ *L*^{1}([0,1]^{m} to be invariant K-minimal with respect to the couple (*L*^{1}([0,1]^{m})), *L*^{∞}([0,1]^{m}) is established. Through this condition, different examples of invariant *K*-minimal sets are constructed. In particular, it is shown that the *L*^{1}-closure of the image of the *L*^{∞}-ball of smooth vector fields with support in (0,1)^{m}, under the divergence operator is an invariant *K*-minimal set. The constructed examples have finite-dimensional analogues in terms of invariant *K*-minimal sets with respect to the couple (ℓ^{1}, ℓ^{∞}) on *R*^{n} . These finite-dimensional analogues are interesting in themselves and connected to applications where the element with minimal *K*-functional is important. We provide a convergent algorithm for computing the element with minimal *K*-functional in these and other finite-dimensional invariant K-minimal sets.

1. Taut Strings and Real Interpolation$(function(){PrimeFaces.cw("OverlayPanel","overlay1045576",{id:"formSmash:j_idt1380:0:j_idt1384",widgetVar:"overlay1045576",target:"formSmash:j_idt1380:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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