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arXiv · 1308.3606

On fractional Laplacians

Roberta Musina·Alexander I. Nazarov
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Abstract

We compare two natural types of fractional Laplacians $(-\Delta)^s$, "Navier" and "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.

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Roberta Musina, Alexander I. Nazarov. 2013-08-16. On fractional Laplacians. https://arxiv.org/abs/1308.3606

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