Relaxation of functionals with linear growth: interactions of emerging measures and free discontinuities
Analysis of PDEs
2021-07-28 v1 Optimization and Control
Abstract
For an integral functional defined on functions featuring a prototypical strong interaction term between and , we calculate its relaxation in the space of functions with bounded variations and Radon measures. Interplay between measures and discontinuities bring various additional difficulties, and concentration effects in recovery sequences play a major role for the relaxed functional even if the limit measures are absolutely continuous with respect to the Lebesgue one.
Keywords
Cite
@article{arxiv.2107.12687,
title = {Relaxation of functionals with linear growth: interactions of emerging measures and free discontinuities},
author = {Stefan Krömer and Martin Kružík and Elvira Zappale},
journal= {arXiv preprint arXiv:2107.12687},
year = {2021}
}