Anisotropic Finsler N-Laplacian Liouville equation in convex cones

2024/07/06 by Wei Dai, Changfeng Gui, Dai, Wei +3 · 1 citation
Mathematics · Physics and Astronomy · #35B06 #35B40 #35J92 #Advanced Differential Geometry Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2407.04987

openalex publication_date 2024/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We consider the anisotropic Finsler N-Laplacian Liouville equation -Δ^H_Nu=e^u \rmin C, where N≥2, C⊆ℝ^N is an open convex cone including ℝ^N, the half space ℝ^N₊ and \frac12^m-space ℝ^N_2^-m:=\x∈ℝ^N| x₁,⋯,x_m>0\ (m=1,⋯,N), and the anisotropic Finsler N-Laplacian Δ^H_N is induced by a positively homogeneous function H(x) of degree 1. All solutions to the Finsler N-Laplacian Liouville equation with finite mass are completely classified. In particular, if H(ξ)=|ξ|, then the Finsler N-Laplacian Δ^H_N reduces to the regular N-Laplacian Δ_N. Our result is a counterpart in the limiting case p=N of the classification results in \citeCFR for the critical anisotropic p-Laplacian equations with 1

Cited by

• Non-radial solutions for the critical quasi-linear Hénon equation involving p-Laplacian in \R^N

Related

• Classification of solutions to the anisotropic N-Liouville equation in ℝ^N
• Extremal solution and Liouville theorem for anisotropic elliptic equations
• Symmetry results for critical anisotropic p-Laplacian equations in\n convex cones
• An exterior overdetermined problem for Finsler N-laplacian in convex cones
• Liouville-type results for some quasilinear anisotropic elliptic equations