A note on Poincaré-Sobolev type inequalities on compact manifolds
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912777479651328 |
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| author | Gicquaud, Romain |
| author_facet | Gicquaud, Romain |
| contents | We prove a Poincaré-Sobolev type inequality on compact Riemannian manifolds where the deviation of a function from a biased average, defined using a density, is controlled by the unweighted Lebesgue norm of its gradient. Unlike classical weighted Poincaré inequalities, the density does not enter the measure or the Sobolev norms, but only the reference average. We show that the associated Poincaré constant depends quantitatively on the Lebesgue norm of the density. This framework naturally arises in the analysis of coupled elliptic systems and seems not to have been addressed in the existing literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_17872 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on Poincaré-Sobolev type inequalities on compact manifolds Gicquaud, Romain Analysis of PDEs Differential Geometry 46E35, 58J05, 35A23 We prove a Poincaré-Sobolev type inequality on compact Riemannian manifolds where the deviation of a function from a biased average, defined using a density, is controlled by the unweighted Lebesgue norm of its gradient. Unlike classical weighted Poincaré inequalities, the density does not enter the measure or the Sobolev norms, but only the reference average. We show that the associated Poincaré constant depends quantitatively on the Lebesgue norm of the density. This framework naturally arises in the analysis of coupled elliptic systems and seems not to have been addressed in the existing literature. |
| title | A note on Poincaré-Sobolev type inequalities on compact manifolds |
| topic | Analysis of PDEs Differential Geometry 46E35, 58J05, 35A23 |
| url | https://arxiv.org/abs/2512.17872 |