Classification of solutions to the anisotropic $N$-Liouville equation in $\mathbb{R}^N$
| Autor: | Ciraolo, Giulio, Li, Xiaoliang |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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]. Comment: The proof of Proposition 3.1 of the previous version contained an error which is corrected in this version |
| Databáze: | arXiv |
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