Calculus of Variations and Geometric Measure Theory
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H. M. Nguyen - M. Squassina

Some remarks on rearrangement for nonlocal functionals

created by squassina on 26 Apr 2017
modified on 10 May 2017

[BibTeX]

Submitted Paper

Inserted: 26 apr 2017
Last Updated: 10 may 2017

Pages: 13
Year: 2017

Abstract:

We prove that a nonlocal functional approximating the standard Dirichlet $p$-norm fails to decrease under two-point rearrangement. Furthermore, we get other properties related to this functional such as decay and compactness.

Keywords: Nonlocal functionals, characterization of Sobolev spaces


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