arXiv:1308.3606 Abstract | arXiv Analytics

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On fractional Laplacians

Published 2013-08-16, updated 2013-10-04Version 2

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.

Comments: 14 pages; this version is considerably enlarged

Categories: math.AP

Subjects: 47A63, 35A23

Keywords: fractional laplacians, natural types, sobolev constants, difference

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