Ground-state blowing-up solutions for a Hardy-Sobolev equations on a manifold
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916860237185024 |
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| author | Ali, Hussein Cheikh Robert, Frédéric |
| author_facet | Ali, Hussein Cheikh Robert, Frédéric |
| contents | We prove the existence of blowing-up families of solutions to an equation of Hardy-Sobolev type in high dimensions. These families are of minimal type. The sole condition is that the potential of the linear operator touches a critical potential at the singular point. This condition is sharp as shown by the first author in [Cheikh-Ali, Pacific J. of Math. 2022]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_05201 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ground-state blowing-up solutions for a Hardy-Sobolev equations on a manifold Ali, Hussein Cheikh Robert, Frédéric Analysis of PDEs 35J60, 58J05 We prove the existence of blowing-up families of solutions to an equation of Hardy-Sobolev type in high dimensions. These families are of minimal type. The sole condition is that the potential of the linear operator touches a critical potential at the singular point. This condition is sharp as shown by the first author in [Cheikh-Ali, Pacific J. of Math. 2022]. |
| title | Ground-state blowing-up solutions for a Hardy-Sobolev equations on a manifold |
| topic | Analysis of PDEs 35J60, 58J05 |
| url | https://arxiv.org/abs/2505.05201 |