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 function, which separates its absolutely continuous part from its singular part (sum of the jump and the Cantorian part). In particular, we prove an 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}
}