Relaxation and Integral Representation for Functionals of Linear Growth on Metric Measure spaces
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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Analysis and Geometry in Metric Spaces, Volume 2016, issue 4, pp. 288–313
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.Description
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Hakkarainen, H, Kinnunen, J, Lahti, P & Lehtelä, P 2016, 'Relaxation and Integral Representation for Functionals of Linear Growth on Metric Measure spaces', Analysis and Geometry in Metric Spaces, vol. 2016, no. 4, 13, pp. 288–313. https://doi.org/10.1515/agms-2016-0013