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arXiv · 1901.09843

Sharp weighted Sobolev trace inequalities and fractional powers of the Laplacian

Jeffrey S. Case
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Abstract

We establish a family of sharp Sobolev trace inequalities involving the $W^{k,2}(\mathbb{R}_+^{n+1},y^a)$-norm. These inequalities are closely related to the realization of fractional powers of the Laplacian on $\mathbb{R}^n=\partial\mathbb{R}_+^{n+1}$ 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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Jeffrey S. Case. 2019-01-28. Sharp weighted Sobolev trace inequalities and fractional powers of the Laplacian. https://doi.org/10.1016/j.jfa.2020.108567

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