A sharp threshold for Trudinger-Moser type inequalities with logarithmic kernels in dimension N
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916580943724544 |
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| author | Cannone, Alessandro Cingolani, Silvia |
| author_facet | Cannone, Alessandro Cingolani, Silvia |
| contents | In the paper we investigate Trudinger-Moser type inequalities in presence of logarithmic kernels in dimension N. A sharp threshold, depending on N, is detected for the existence of estremal functions or blow-up, where the domain is the ball or the entire space. We also show that the extremal functions satisfy suitable Euler-Lagrange equations. When the domain is the entire space, such equation can be derived by N-Laplacian Schrodinger equation strongly coupled with a higher order fractional Poisson's equation. The results extends [16] to any dimension N bigger than 2. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_10013 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A sharp threshold for Trudinger-Moser type inequalities with logarithmic kernels in dimension N Cannone, Alessandro Cingolani, Silvia Analysis of PDEs 35J60, 35Q40, 31B10, 35B33 In the paper we investigate Trudinger-Moser type inequalities in presence of logarithmic kernels in dimension N. A sharp threshold, depending on N, is detected for the existence of estremal functions or blow-up, where the domain is the ball or the entire space. We also show that the extremal functions satisfy suitable Euler-Lagrange equations. When the domain is the entire space, such equation can be derived by N-Laplacian Schrodinger equation strongly coupled with a higher order fractional Poisson's equation. The results extends [16] to any dimension N bigger than 2. |
| title | A sharp threshold for Trudinger-Moser type inequalities with logarithmic kernels in dimension N |
| topic | Analysis of PDEs 35J60, 35Q40, 31B10, 35B33 |
| url | https://arxiv.org/abs/2410.10013 |