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On fractional Laplacians (1308.3606v2)
Published 16 Aug 2013 in math.AP
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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