
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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License | CC BY-NC-ND 4.0 (Attribution-NonCommercial-NoDerivatives) |
Work Type | Article |
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Publication Date | September 2020 |
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Deposited | September 09, 2021 |
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