Calculus of Variations and Geometric Measure Theory

K. Mohanta - F. Sk

On the best constant in fractional $p$-Poincaré inequalities on cylindrical domains

created by sk on 21 Nov 2021
modified on 22 Dec 2022

[BibTeX]

Published Paper

Inserted: 21 nov 2021
Last Updated: 22 dec 2022

Journal: Differential and Integral Equations
Year: 2021
Doi: 10.57262/die034-1112-691

ArXiv: 2103.16845 PDF

Abstract:

We investigate the best constants for the regional fractional $p$-Poincaré inequality and the fractional p-Poincaré inequality in cylindrical domains. For the special case $p=2$, the result was already known due to Chowdhury-Csató-Roy-Sk Study of fractional Poincaré inequalities on unbounded domains, Discrete Contin. Dyn. Syst., 41(6), 2021. We addressed the asymptotic behavior of the first eigenvalue of the nonlocal Dirichlet p-Laplacian eigenvalue problem when the domain is becoming unbounded in several directions.