Some remarks on rearrangement for nonlocal functionals
Functional Analysis
2017-05-11 v2
Abstract
We prove that a nonlocal functional approximating the standard Dirichlet -norm fails to decrease under two-point rearrangement. Furthermore, we get other properties related to this functional such as decay and compactness, and the Polya-Szeg\"o inequality for Riesz fractional gradients, a notion recently introduced in the literature.
Cite
@article{arxiv.1704.08077,
title = {Some remarks on rearrangement for nonlocal functionals},
author = {Hoai-Minh Nguyen and Marco Squassina},
journal= {arXiv preprint arXiv:1704.08077},
year = {2017}
}
Comments
12 pages