On fractional Laplacians -- 2

Abstract

The present paper is the natural evolution of arXiv:1308.3606. For $s>-1$ we compare two natural types of fractional Laplacians $(-\Delta {)}^s$, namely, the "Navier" and the "Dirichlet" ones. As a main tool, we give the "dual" Caffarelli--Silvestre and Stinga--Torrea variational characterizations of these operators for $s\in (-1,0)$.

9 pages; some references are added; a small generalization is given