Symmetric radial decreasing rearrangement can increase the fractional Gagliardo norm in domains

TL;DR

This paper demonstrates that applying symmetric radial decreasing rearrangement to functions can lead to an increase in their fractional Gagliardo semi-norm within certain domains, challenging previous assumptions about rearrangement effects.

Contribution

It is the first to show that symmetric radial decreasing rearrangement can increase the fractional Gagliardo semi-norm in domains, revealing new properties of function rearrangements.

Findings

Rearrangement can increase fractional Gagliardo semi-norms

Challenged assumptions about rearrangement effects

Provides new insights into function analysis

Abstract

We show that the symmetric radial decreasing rearrangement can increase the fractional Gagliardo semi-norm in domains.