Inserted: 21 nov 2021
Journal: Differential and Integral Equations
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.