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arXiv · 2411.18188

A note on P\'{o}lya-Szeg\"{o} inequality for fractional Orlicz-Sobolev seminorm in domains

Remi Yvant Temgoua
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Abstract

In this paper, we study the effect of symmetric radial decreasing rearrangement on fractional Orlicz-Sobolev seminorm in domains. Roughly speaking, we prove that symmetric radial decreasing rearrangement can increase the fractional Orlicz-Sobolev seminorm in domains. Our result extends that of Li-Wang [Commun. Contemp. Math. 21.07 (2019): 1850059.] to the setting of fractional seminorm in domains admitting behaviors more general than powers.

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Remi Yvant Temgoua. 2024-11-27. A note on P\'{o}lya-Szeg\"{o} inequality for fractional Orlicz-Sobolev seminorm in domains. https://arxiv.org/abs/2411.18188

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