English

Limiting case Hardy inequalities on the sphere

Analysis of PDEs 2017-11-03 v1

Abstract

We give sharp limiting case Hardy inequalities on the sphere S2\mathbb{S}^{2} and show that their optimal constants are unattainable by any fH1(S2){0}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.

Keywords

Cite

@article{arxiv.1711.00724,
  title  = {Limiting case Hardy inequalities on the sphere},
  author = {Ahmed A. Abdelhakim},
  journal= {arXiv preprint arXiv:1711.00724},
  year   = {2017}
}
R2 v1 2026-06-22T22:34:00.270Z