On the continuity of functionals defined on partitions
Functional Analysis
2016-12-07 v1
Abstract
We characterize the continuity of prototypical functionals acting on finite Caccioppoli partitions. In the spirit of the classical Reshetnyak continuity theorem for measures that can be used to prove continuity of surface-type functionals defined on single sets of finite perimeter we show that in the multiphase case continuity is equivalent to convergence of the perimeter of the jump set.
Cite
@article{arxiv.1612.01781,
title = {On the continuity of functionals defined on partitions},
author = {Matthias Ruf},
journal= {arXiv preprint arXiv:1612.01781},
year = {2016}
}
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5 pages