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arXiv · 2107.08647

Almost sharp Sobolev trace inequalities in the unit ball under constraints

Xuezhang Chen·Wei Wei·Nan Wu
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Abstract

We establish three families of Sobolev trace inequalities of orders two and four in the unit ball under higher order moments constraint, and are able to construct \emph{smooth} test functions to show all such inequalities are \emph{almost optimal}. Some distinct feature in \emph{almost sharpness} examples between the fourth order and second order Sobolev trace inequalities is discovered. This has been neglected in higher order Sobolev inequality case in \cite{Hang}. As a byproduct, the method of our construction can be used to show the sharpness of the generalized Lebedev-Milin inequality under constraints.

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Xuezhang Chen, Wei Wei, Nan Wu. 2022-01-25. Almost sharp Sobolev trace inequalities in the unit ball under constraints. https://arxiv.org/abs/2107.08647

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