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arXiv · 2306.12039

Classification of solutions to the anisotropic $N$-Liouville equation in $\mathbb{R}^N$

Giulio Ciraolo·Xiaoliang Li
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Abstract

Given $N\geq 2$, we completely classify the solutions of the anisotropic $N$-Liouville equation $$-\Delta_N^H\,u=e^u \quad\text{in }\mathbb{R}^N,$$ under the finite mass condition $\int_{\mathbb{R}^N} e^u\,dx<+\infty$. Here $\Delta_N^H$ is the so-called Finsler $N$-Laplacian induced by a positively homogeneous function $H$. As a consequence for $N=2$, we give an affirmative answer to a conjecture made in [G. Wang and C. Xia, J. Differential Equations 252 (2012) 1668--1700].

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Giulio Ciraolo, Xiaoliang Li. 2023-06-21. Classification of solutions to the anisotropic $N$-Liouville equation in $\mathbb{R}^N$. https://arxiv.org/abs/2306.12039

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