Quantitative stability for the Trudinger-Moser inequality
Fuente:
arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866918484697415680 |
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| author | Andrade, João Henrique de Oliveira, José Francisco Ò, João Marcos do Macedo, Abiel Costa Ratzkin, Jesse |
| author_facet | Andrade, João Henrique de Oliveira, José Francisco Ò, João Marcos do Macedo, Abiel Costa Ratzkin, Jesse |
| contents | We establich quantitative stability estimates for the Trudinger-Moser inequality on smooth, bounded domains in the Euclidean plane. More specifically, we prove that the deficit in the Trudinger-Moser inequality quadratically controls the distance to the set of optimizers if either (i) the exponential rate of growth is sufficiently small or (ii) the domain is a round disk. The latter estimate remains valid even in the critical case. Both proofs rely on a new spectral gap that we prove, which may be of independent interest. Additionally we show that the same stability estimate holds in the nondegenerate case, and that this occurs generically. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03668 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantitative stability for the Trudinger-Moser inequality Andrade, João Henrique de Oliveira, José Francisco Ò, João Marcos do Macedo, Abiel Costa Ratzkin, Jesse Analysis of PDEs We establich quantitative stability estimates for the Trudinger-Moser inequality on smooth, bounded domains in the Euclidean plane. More specifically, we prove that the deficit in the Trudinger-Moser inequality quadratically controls the distance to the set of optimizers if either (i) the exponential rate of growth is sufficiently small or (ii) the domain is a round disk. The latter estimate remains valid even in the critical case. Both proofs rely on a new spectral gap that we prove, which may be of independent interest. Additionally we show that the same stability estimate holds in the nondegenerate case, and that this occurs generically. |
| title | Quantitative stability for the Trudinger-Moser inequality |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2605.03668 |