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

Heikki 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 -