Work

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

Year: 2026

Type: preprint

Abstract: Let $10$, 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 $0m$ follows from the theorem of Lu and Zhu.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.30006

Authors: Wu, Tian, Yan, Jin, Zhu, Hua

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Southwest University of Science and Technology, Fundamental Research Funds for the Central Universities, Division of Mathematical Sciences

Award: G9000363445

OpenAlex ID: W7214279550

Cites: 24

Cited by: 1

Related to: 10