Relaxation and integral representation for functionals of linear growth on metric measure spaces
Functional Analysis
2014-01-23 v1
Abstract
This article studies an integral representation of functionals of linear growth on metric measure spaces with a doubling measure and a Poincar\'e 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.
Keywords
Cite
@article{arxiv.1401.5717,
title = {Relaxation and integral representation for functionals of linear growth on metric measure spaces},
author = {Heikki Hakkarainen and Juha Kinnunen and Panu Lahti and Pekka Lehtelä},
journal= {arXiv preprint arXiv:1401.5717},
year = {2014}
}