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arXiv · 1903.03190

A P\'olya-Szeg\"o principle for general fractional Orlicz-Sobolev spaces

Pablo de Nápoli·Julián Fernández Bonder·Ariel Salort
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Abstract

In this article we prove modular and norm P\'olya-Szeg\"o inequalities in general fractional Orlicz-Sobolev spaces by using the polarization technique. We introduce a general framework which includes the different definitions of theses spaces in the literature, and we establish some of its basic properties such as the density of smooth functions. As a corollary we prove a Rayleigh-Faber-Krahn type inequality for Dirichlet eigenvalues under nonlocal nonstandard growth operators.

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Pablo de Nápoli, Julián Fernández Bonder, Ariel Salort. 2019-03-07. A P\'olya-Szeg\"o principle for general fractional Orlicz-Sobolev spaces. https://arxiv.org/abs/1903.03190

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