# Relaxation and Integral Representation for Functionals of Linear Growth on Metric Measure spaces

Heikki Hakkarainen; Juha Kinnunen; Panu Lahti; Pekka Lehtelä

Analysis and Geometry in Metric Spaces (2016)

- Volume: 4, Issue: 1, page 288-313, electronic only
- ISSN: 2299-3274

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topHeikki Hakkarainen, et al. "Relaxation and Integral Representation for Functionals of Linear Growth on Metric Measure spaces." Analysis and Geometry in Metric Spaces 4.1 (2016): 288-313, electronic only. <http://eudml.org/doc/287109>.

@article{HeikkiHakkarainen2016,

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.},

author = {Heikki Hakkarainen, Juha Kinnunen, Panu Lahti, Pekka Lehtelä},

journal = {Analysis and Geometry in Metric Spaces},

keywords = {calculus of variations; functionals of linear growth; relaxation; functions of bounded variation; analysis on metric measure spaces; functionals; integral representation; linear growth; metric measure spaces},

language = {eng},

number = {1},

pages = {288-313, electronic only},

title = {Relaxation and Integral Representation for Functionals of Linear Growth on Metric Measure spaces},

url = {http://eudml.org/doc/287109},

volume = {4},

year = {2016},

}

TY - JOUR

AU - Heikki Hakkarainen

AU - Juha Kinnunen

AU - Panu Lahti

AU - Pekka Lehtelä

TI - Relaxation and Integral Representation for Functionals of Linear Growth on Metric Measure spaces

JO - Analysis and Geometry in Metric Spaces

PY - 2016

VL - 4

IS - 1

SP - 288

EP - 313, electronic only

AB - 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.

LA - eng

KW - calculus of variations; functionals of linear growth; relaxation; functions of bounded variation; analysis on metric measure spaces; functionals; integral representation; linear growth; metric measure spaces

UR - http://eudml.org/doc/287109

ER -

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