The Eigenvalue Problem for the Regional Fractional Laplacian in the Small Order Limit

Abstract In this note, we study the asymptotic behavior of eigenvalues and eigenfunctions regional fractional Laplacian $(-{\Delta })^{s}_{\Omega }$ ( ? ? ) ? s as $s\rightarrow 0^{+}.$ ? 0 + . Our analysis leads to a logarithmic Laplacian, which arises formal derivative Laplacians at s = 0.