Relaxation and Integral Representation for Functionals of Linear Growth on Metric Measure spaces
Abstract: This article studies an integral representation of functionals of linear growth on metric measure spaces with a doubling measure and a Poincaré inequality. Such a functional is defined via relaxation, and it defines a Radon measure on the space. For the singular part of the functional, we get the expected integral representation with respect to the variation measure. A new feature is that in the representation for the absolutely continuous part, a constant appears already in the weighted Euclidean case. As an application we show that in a variational minimization problem involving the functional, boundary values can be presented as a penalty term.
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- Extent
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Online-Ressource
- Language
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Englisch
- Bibliographic citation
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Relaxation and Integral Representation for Functionals of Linear Growth on Metric Measure spaces ; volume:4 ; number:1 ; year:2016 ; extent:26
Analysis and geometry in metric spaces ; 4, Heft 1 (2016) (gesamt 26)
- Creator
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Hakkarainen, Heikki
Kinnunen, Juha
Lahti, Panu
Lehtelä, Pekka
- DOI
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10.1515/agms-2016-0013
- URN
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urn:nbn:de:101:1-2024041116315871017321
- Rights
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
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14.08.2025, 11:03 AM CEST
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Associated
- Hakkarainen, Heikki
- Kinnunen, Juha
- Lahti, Panu
- Lehtelä, Pekka
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