Trudinger-Moser type inequalities for the Hessian equation with logarithmic weights
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912324666785792 |
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| author | Ó, João Marcos do de Oliveira, José Francisco Ponciano, Raoní Cabral |
| author_facet | Ó, João Marcos do de Oliveira, José Francisco Ponciano, Raoní Cabral |
| contents | We establish sharp Trudinger-Moser inequalities with logarithmic weights for the $k$-Hessian equation and investigate the existence of maximizers. Our analysis extends the classical results of Tian and Wang to $k$-admissible function spaces with logarithmic weights, providing a natural complement to the work of Calanchi and Ruf. Our approach relies on transforming the problem into a one-dimensional weighted Sobolev space, where we solve it using various techniques, including some radial lemmas and certain Hardy-type inequalities, which we establish in this paper, as well as a theorem due to Leckband. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_09295 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Trudinger-Moser type inequalities for the Hessian equation with logarithmic weights Ó, João Marcos do de Oliveira, José Francisco Ponciano, Raoní Cabral Analysis of PDEs 35J60, 35B33, 46E35, 26D10 We establish sharp Trudinger-Moser inequalities with logarithmic weights for the $k$-Hessian equation and investigate the existence of maximizers. Our analysis extends the classical results of Tian and Wang to $k$-admissible function spaces with logarithmic weights, providing a natural complement to the work of Calanchi and Ruf. Our approach relies on transforming the problem into a one-dimensional weighted Sobolev space, where we solve it using various techniques, including some radial lemmas and certain Hardy-type inequalities, which we establish in this paper, as well as a theorem due to Leckband. |
| title | Trudinger-Moser type inequalities for the Hessian equation with logarithmic weights |
| topic | Analysis of PDEs 35J60, 35B33, 46E35, 26D10 |
| url | https://arxiv.org/abs/2504.09295 |