Weighted Hardy inequality on Riemannian manifolds (Q2828649)
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scientific article; zbMATH DE number 6643602
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Weighted Hardy inequality on Riemannian manifolds |
scientific article; zbMATH DE number 6643602 |
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Weighted Hardy inequality on Riemannian manifolds (English)
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26 October 2016
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weighted Hardy inequality
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existence
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non-existence
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Fermi coordinates
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Given a smooth compact Riemannian manifold \((\mathcal M,g)\) of dimension \(N\geq3\), let \(\Sigma\) be a closed submanifold of dimension \(k\in[1,N-2]\). Following \textit{H. Brézis} et al. [J. Funct. Anal. 171, No. 1, 177--191 (2000; Zbl 0953.26006)], the author studies existence and non-existence of minimizers to the Hardy inequality with weight function that is singular on \(\Sigma\), and proves necessary and sufficient conditions for the existence of minimizers.
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