On fractional Laplacians

Roberta Musina; Alexander I. Nazarov

On fractional Laplacians

Analysis of PDEs 2013-10-08 v2

Authors: Roberta Musina , Alexander I. Nazarov

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.

Keywords

fractional laplacian

Cite

@article{arxiv.1308.3606,
  title  = {On fractional Laplacians},
  author = {Roberta Musina and Alexander I. Nazarov},
  journal= {arXiv preprint arXiv:1308.3606},
  year   = {2013}
}

Comments

14 pages; this version is considerably enlarged

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