Calculus of Variations and Geometric Measure Theory

I. Chowdhury - G. Csato - P. Roy - F. Sk

Study of fractional Poincaré inequalities on unbounded domains

created by csato on 12 Nov 2021
modified by sk on 22 Nov 2021


Published Paper

Inserted: 12 nov 2021
Last Updated: 22 nov 2021

Journal: Discrete Continuous Dynam. Syst .
Year: 2019

ArXiv: 1904.07170 PDF


The central aim of this paper is to study (regional) fractional Poincar\'e 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 Poincar\'e 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}.