Limiting case Hardy inequalities on the sphere
Abstract
We give sharp limiting case Hardy inequalities on the sphere $\mathbb{S}^{2}$ and show that their optimal constants are unattainable by any $f\in H^{1}\left(\mathbb{S}^{2}\right)\setminus\{0\}$. The singularity of the problem is related to the geodesic distance from a point on the sphere.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2017
- DOI:
- 10.48550/arXiv.1711.00724
- arXiv:
- arXiv:1711.00724
- Bibcode:
- 2017arXiv171100724A
- Keywords:
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- Mathematics - Analysis of PDEs