On fractional Laplacians

Published 16 Aug 2013 in math.AP | (1308.3606v2)

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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