We compare two natural types of fractional Laplacians (- Δ)s, namely, the "Navier" and the "Dirichlet" ones. We show that for 0 < s < 1 their difference is positive definite and positivity preserving. Then we prove the coincidence of the Sobolev constants for these two fractional Laplacians.
On Fractional Laplacians
MUSINA, Roberta;
2014-01-01
Abstract
We compare two natural types of fractional Laplacians (- Δ)s, namely, the "Navier" and the "Dirichlet" ones. We show that for 0 < s < 1 their difference is positive definite and positivity preserving. Then we prove the coincidence of the Sobolev constants for these two fractional Laplacians.File in questo prodotto:
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