Liouville Theorem for Quasilinear Elliptic Equations in ℝ^N

Abstract

We prove Liouville theorem for the equation Δ_mv + v^p + M∣∇v∣^q = 0 in a domain Ω ⊂ ℝⁿ, with M ∈ ℝ in the critical and subcritical case. As a natural extension of our recent work [2023, arXiv:2311.04641], the proof is based on an integral identity and Young’s inequality.

Keywords

Liouville theorem / quasilinear elliptic equation / p-Laplacian / 35J62

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Peking University