Liouville theorem for elliptic equations involving the sum of the function and its gradient in \mathbb Rⁿ

2023/11/08 by Xi-nan Ma, Ma, Xi-Nan, Wangzhe Wu +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2311.04641

openalex publication_date 2023/11/08 · openalex created_date 2023/11/10 · openalex updated_date 2026/07/28

Abstract

We prove Liouville theorem for the equation Δv + N v^p + M |∇ v|^q= 0 in \mathbb Rⁿ, with M, N > 0, q = (2p)/(p + 1) in the critical and subcritical case. The proof is based on a differential identity and Young inequality. We remark that this is the second version for the paper. And we thank Prof. Bidaut-Véron and Véron for their very useful comments on this paper. Compared with the first one, in this version we correct some errors and adjust the arrangement of the proof so that it can be understood easily.

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