Stability for the Sobolev inequality in cones
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912233556017152 |
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| author | Pacella, Filomena Ciraolo, Giulio Polvara, Camilla Chiara |
| author_facet | Pacella, Filomena Ciraolo, Giulio Polvara, Camilla Chiara |
| contents | We prove a quantitative Sobolev inequality in cones of Bianchi-Egnell type, which implies a stability property. Our result holds for any cone as long as the minimizers of the Sobolev quotient are nondegenerate, which is the case of most cones. When the minimizers are the classical bubbles we have more precise results. Finally, we show that local estimates are not enough to get the optimal constant for the quantitative Sobolev inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_11087 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability for the Sobolev inequality in cones Pacella, Filomena Ciraolo, Giulio Polvara, Camilla Chiara Analysis of PDEs 49J40, 26D10, 35A23, 35J91, 35B33 We prove a quantitative Sobolev inequality in cones of Bianchi-Egnell type, which implies a stability property. Our result holds for any cone as long as the minimizers of the Sobolev quotient are nondegenerate, which is the case of most cones. When the minimizers are the classical bubbles we have more precise results. Finally, we show that local estimates are not enough to get the optimal constant for the quantitative Sobolev inequality. |
| title | Stability for the Sobolev inequality in cones |
| topic | Analysis of PDEs 49J40, 26D10, 35A23, 35J91, 35B33 |
| url | https://arxiv.org/abs/2502.11087 |