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

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 $$-Q_N{u}_n=V_n{e}^{u_n}\text{quadin}\mathrm{\Omega }\subset {\mathbb{R}}^N,N\ge 2.$$ 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 ${\mathbb{R}}^N$ ($N\ge 3$) in their recent paper [CVPDE, 2024].