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.
Original language | English |
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Article number | 13 |
Pages (from-to) | 288–313 |
Journal | ANALYSIS AND GEOMETRY IN METRIC SPACES |
Volume | 2016 |
Issue number | 4 |
DOIs | |
Publication status | Published - 2016 |
MoE publication type | A1 Journal article-refereed |
Keywords
- calculus of variations
- functionals of linear growth
- relaxation
- functions of bounded variation
- analysis on metric measure spaces