Abstract

The present paper is the natural evolution of arXiv:1308.3606. For s>−1s>-1 we compare two natural types of fractional Laplacians (−Δ)s(-Δ)^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∈(−1,0)s\in(-1,0).

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