Study of fractional Poincaré inequalities on unbounded domains

Abstract

The central aim of this paper is to study (regional) fractional Poincaré type inequalities on unbounded domains satisfying the finite ball condition. Both existence and non existence type results are established depending on various conditions on domains and on the range of $s\in (0,1)$. The best constant in both regional fractional and fractional Poincaré inequality is characterized for strip like domains $(\omega \times {\mathbb{R}}^{n-1})$, and the results obtained in this direction are analogous to those of the local case. This settles one of the natural questions raised by K. Yeressian in [\textit{Asymptotic behavior of elliptic nonlocal equations set in cylinders, Asymptot. Anal. 89, (2014), no 1-2}].

arXiv comment23 pages

References in corpus (4)

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• On the Asymptotic Analysis of Problems Involving Fractional Laplacian in Cylindrical Domains Tending to Infinity
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Cited by in corpus (4)

• Hardy and Poincaré inequalities in fractional Orlicz-Sobolev spaces
• Fractional Poincaré Inequality for Unbounded Domains with Finite Ball Condition: Counter Example
• Remarks on the fractional Moser-Trudinger inequality
• Asymptotic analysis of the Dirichlet fractional Laplacian in domains becoming unbounded