Quantization of blow-up masses for the Finsler N-Liouville equation

2025/08/22 by Huang, Xia, Li, Yuan, Ye, Dong +1
#35B44 #35J92 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.16080

Abstract

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_Nu_n=V_ne^u_n\quadin~ Ω⊂ ℝ^N, N ≥ 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 ℝ² [JDE, 2012], and Esposito-Lucia's for the N-Laplacian case in ℝ^N (N ≥ 3) in their recent paper [CVPDE, 2024].

Citations

• Harnack inequalities and quantization properties for the n-Liouville\n equation
• A classification result for the quasi-linear Liouville equation
• On a quasilinear mean field equation with exponential nonlinearity

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