English

On the gradient rearrangement of functions

Analysis of PDEs 2024-04-30 v2

Abstract

In this paper, we introduce a symmetrization technique for the gradient of a \BV\BV function, which separates its absolutely continuous part from its singular part (sum of the jump and the Cantorian part). In particular, we prove an L1\text{\emph{L}}^{\text{1}} comparison between the function and its symmetrized. Furthermore, we apply this result to obtain Saint-Venant type inequalities for some geometric functionals.

Keywords

Cite

@article{arxiv.2302.11332,
  title  = {On the gradient rearrangement of functions},
  author = {Vincenzo Amato and Andrea Gentile and Carlo Nitsch and Cristina Trombetti},
  journal= {arXiv preprint arXiv:2302.11332},
  year   = {2024}
}