Sharp Onofri trace inequality on the upper half space and quasi-linear Liouville equation with Neumann boundary
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914049756758016 |
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| author | Dou, Jingbo Han, Yazhou Yuan, Shuang Zhou, Yang |
| author_facet | Dou, Jingbo Han, Yazhou Yuan, Shuang Zhou, Yang |
| contents | In this paper, we establish a sharp Onofri trace inequality on the upper half space $\overline{\mathbb R_+^n} (n\geq 2)$ by considering the limiting case of Sobolev trace inequality and classify its extremal functions on a suitable weighted Sobolev space. For this aim, by the Serrin-Zou type identity and the Pohozaev type identity, we show the classification of the solutions for a quasi-linear Liouville equation with Neumann boundary which is closely related to the Euler-Lagrange equation of the Onofri trace inequality and it has independent research value. The regularity and asymptotic estimates of solutions to the above equation are essential to discuss. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_17031 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sharp Onofri trace inequality on the upper half space and quasi-linear Liouville equation with Neumann boundary Dou, Jingbo Han, Yazhou Yuan, Shuang Zhou, Yang Analysis of PDEs 26D10, 35B08, 35B40, 35J92, 35B53, 35J66 In this paper, we establish a sharp Onofri trace inequality on the upper half space $\overline{\mathbb R_+^n} (n\geq 2)$ by considering the limiting case of Sobolev trace inequality and classify its extremal functions on a suitable weighted Sobolev space. For this aim, by the Serrin-Zou type identity and the Pohozaev type identity, we show the classification of the solutions for a quasi-linear Liouville equation with Neumann boundary which is closely related to the Euler-Lagrange equation of the Onofri trace inequality and it has independent research value. The regularity and asymptotic estimates of solutions to the above equation are essential to discuss. |
| title | Sharp Onofri trace inequality on the upper half space and quasi-linear Liouville equation with Neumann boundary |
| topic | Analysis of PDEs 26D10, 35B08, 35B40, 35J92, 35B53, 35J66 |
| url | https://arxiv.org/abs/2509.17031 |