Nonlinear Neumann boundary problems for $n$-Laplacian Liouville equation on a half space
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910013996400640 |
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| author | Dai, Wei Gui, Changfeng Hu, Yichen Peng, Shaolong |
| author_facet | Dai, Wei Gui, Changfeng Hu, Yichen Peng, Shaolong |
| contents | In this paper, for general $n\geq2$, we classify solutions to $n$-Laplacian Liouville equation with positive nonlinear Neumann boundary condition on the half-space $\mathbb{R}^{n}_{+}$. Under the positive nonlinear Neumann boundary condition, our result extend the classification result for the second order Liouville equation in \cite{Li} from $n=2$ to general $n\geq2$, and also extend the classification result for critical $p$-Laplacian equation in \cite{Zhou} from $p<n$ to $p=n$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_06414 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nonlinear Neumann boundary problems for $n$-Laplacian Liouville equation on a half space Dai, Wei Gui, Changfeng Hu, Yichen Peng, Shaolong Analysis of PDEs Differential Geometry 35J92, 35B06, 35B40 In this paper, for general $n\geq2$, we classify solutions to $n$-Laplacian Liouville equation with positive nonlinear Neumann boundary condition on the half-space $\mathbb{R}^{n}_{+}$. Under the positive nonlinear Neumann boundary condition, our result extend the classification result for the second order Liouville equation in \cite{Li} from $n=2$ to general $n\geq2$, and also extend the classification result for critical $p$-Laplacian equation in \cite{Zhou} from $p<n$ to $p=n$. |
| title | Nonlinear Neumann boundary problems for $n$-Laplacian Liouville equation on a half space |
| topic | Analysis of PDEs Differential Geometry 35J92, 35B06, 35B40 |
| url | https://arxiv.org/abs/2602.06414 |