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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.16080 |
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| _version_ | 1866909748722401280 |
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| author | Huang, Xia Li, Yuan Ye, Dong Zhou, Feng |
| author_facet | Huang, Xia Li, Yuan Ye, Dong Zhou, Feng |
| contents | The quantization results for blow-up phenomena play crucial roles in the analysis of partial differential equations. Here we quantify the blow-up masses to the following Finsler $N$-Liouville equation $$-Q_{N}u_{n}=V_{n}e^{u_{n}}\quad\mbox{in}~ Ω\subset \mathbb{R}^{N}, N \ge 2.$$ Our study generalizes the classical result of Li-Shafrir [Indiana Univ. Math.J.,1994] for Liouville equation, Wang-Xia's work for anisotropic Liouville equation in $\mathbb{R}^2$ [JDE, 2012], and Esposito-Lucia's for the $N$-Laplacian case in $\mathbb{R}^N$ ($N \geq 3$) in their recent paper [CVPDE, 2024]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_16080 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantization of blow-up masses for the Finsler $N$-Liouville equation Huang, Xia Li, Yuan Ye, Dong Zhou, Feng Analysis of PDEs 35B44, 35J92 The quantization results for blow-up phenomena play crucial roles in the analysis of partial differential equations. Here we quantify the blow-up masses to the following Finsler $N$-Liouville equation $$-Q_{N}u_{n}=V_{n}e^{u_{n}}\quad\mbox{in}~ Ω\subset \mathbb{R}^{N}, N \ge 2.$$ Our study generalizes the classical result of Li-Shafrir [Indiana Univ. Math.J.,1994] for Liouville equation, Wang-Xia's work for anisotropic Liouville equation in $\mathbb{R}^2$ [JDE, 2012], and Esposito-Lucia's for the $N$-Laplacian case in $\mathbb{R}^N$ ($N \geq 3$) in their recent paper [CVPDE, 2024]. |
| title | Quantization of blow-up masses for the Finsler $N$-Liouville equation |
| topic | Analysis of PDEs 35B44, 35J92 |
| url | https://arxiv.org/abs/2508.16080 |