Liouville theorem for quasilinear elliptic equations in \mathbb R^N

2023/11/22 by Wangzhe Wu, Wu, Wangzhe, Qiqi Zhang +1
Computer Science · Mathematics · Engineering · #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2311.13418

Abstract

We prove Liouville theorem for the equation Δ_m v + v^p + M |∇ v|^q= 0 in a domain Ω⊂\mathbb Rⁿ, with M∈ ℝ in the critical and subcritical case. As a natural extension of our recent work \citeMWZ, the proof is based on an integral identity and Young's inequality.

Related

• Liouville theorem for elliptic equations involving the sum of the function and its gradient in \mathbb Rⁿ
• Liouville theorem for elliptic equations with a source reaction term involving the product of the function and its gradient in \mathbb Rⁿ
• A priori estimates and Liouville type results for quasilinear elliptic equations involving gradient terms
• Liouville properties for differential inequalities with (p,q) Laplacian operator
• A Liouville theorem for non local elliptic equations