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Mathematics > Functional Analysis

arXiv:1401.5717 (math)
[Submitted on 22 Jan 2014]

Title:Relaxation and integral representation for functionals of linear growth on metric measure spaces

Authors:Heikki Hakkarainen, Juha Kinnunen, Panu Lahti, Pekka Lehtelä
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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 through 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 related to the functional, boundary values can be presented as a penalty term.
Subjects: Functional Analysis (math.FA)
MSC classes: 49Q20, 30L99, 26B30
Cite as: arXiv:1401.5717 [math.FA]
  (or arXiv:1401.5717v1 [math.FA] for this version)
  https://doi.org/10.48550/arXiv.1401.5717

Submission history

From: Panu Lahti [view email]
[v1] Wed, 22 Jan 2014 16:15:05 UTC (28 KB)
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