English

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 (u,v)W1,1×L1(u,v)\in W^{1,1}\times L^1 featuring a prototypical strong interaction term between uu and vv, 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}
}