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 of the regional fractional Laplacian $(-\Delta {)}^s$ as $s\to 0^{+}$. Our analysis leads to a study of the regional logarithmic Laplacian, which arises as a formal derivative of regional fractional Laplacians at $s=0$.