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