Sharp weighted Sobolev trace inequalities and fractional powers of the Laplacian

We establish a family of sharp Sobolev trace inequalities involving the Wk,2(R+n+1,ya)-norm. These inequalities are closely related to the realization of fractional powers of the Laplacian on Rn=∂R+n+1 as generalized Dirichlet-to-Neumann operators associated to powers of the weighted Laplacian in upper half space, generalizing observations of Caffarelli–Silvestre and of Yang.

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Work Title Sharp weighted Sobolev trace inequalities and fractional powers of the Laplacian
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Open Access
Creators
  1. Jeffrey S. Case
License CC BY-NC-ND 4.0 (Attribution-NonCommercial-NoDerivatives)
Work Type Article
Publisher
  1. Elsevier BV
Publication Date September 2020
Publisher Identifier (DOI)
  1. 10.1016/j.jfa.2020.108567
Source
  1. Journal of Functional Analysis
Deposited September 09, 2021

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