Nonlinear Neumann boundary problems for $n$-Laplacian Liouville equation on a half space

Fuente: arXiv
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Main Authors: Dai, Wei, Gui, Changfeng, Hu, Yichen, Peng, Shaolong
Format: Preprint
Published: 2026
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_version_ 1866910013996400640
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
id 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