Moser-Trudinger inequalities: from local to global
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909286262636544 |
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| author | Fontana, Luigi Morpurgo, Carlo Qin, Liuyu |
| author_facet | Fontana, Luigi Morpurgo, Carlo Qin, Liuyu |
| contents | Given a general complete Riemannian manifold $M$, we introduce the concept of "local Moser-Trudinger inequality on $W^{1,n}(M)$". We show how the validity of the Moser-Trudinger inequality can be extended from a local to a global scale under additional assumptions: either by assuming the validity of the Poincaré inequality, or by imposing a stronger norm condition. We apply these results to Hadamard manifolds. The technique is general enough to be applicable also in sub-Riemannian settings, such as the Heisenberg group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06989 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Moser-Trudinger inequalities: from local to global Fontana, Luigi Morpurgo, Carlo Qin, Liuyu Analysis of PDEs 46E35, 26D10 Given a general complete Riemannian manifold $M$, we introduce the concept of "local Moser-Trudinger inequality on $W^{1,n}(M)$". We show how the validity of the Moser-Trudinger inequality can be extended from a local to a global scale under additional assumptions: either by assuming the validity of the Poincaré inequality, or by imposing a stronger norm condition. We apply these results to Hadamard manifolds. The technique is general enough to be applicable also in sub-Riemannian settings, such as the Heisenberg group. |
| title | Moser-Trudinger inequalities: from local to global |
| topic | Analysis of PDEs 46E35, 26D10 |
| url | https://arxiv.org/abs/2408.06989 |