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; Nazarov, A. I.. - In: COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0360-5302. - 39:9(2014), pp. 1780-1790. [10.1080/03605302.2013.864304]
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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