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arXiv · 2609.30006

The $m$-Laplace equation with a gradient term I: Liouville theorem in the second subcritical case

Tian Wu·Jin Yan·Hua Zhu
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Abstract

Let $1 0$, and $p\in\mathbb R$. We study positive $C^1_{\mathrm{loc}}$ weak solutions of \[-Δ_m u=u^p|Du|^q\qquad\text{in }\mathbb R^n.\] If $0 m$ follows from the theorem of Lu and Zhu.

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Tian Wu, Jin Yan, Hua Zhu. 2026-09-24. The $m$-Laplace equation with a gradient term I: Liouville theorem in the second subcritical case. https://arxiv.org/abs/2609.30006

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