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|
|License||CC BY-NC-ND 4.0 (Attribution-NonCommercial-NoDerivatives)|
|Publication Date||September 2020|
|Publisher Identifier (DOI)||
|Deposited||September 09, 2021|
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