A Liouville theorem for high order degenerate elliptic equations

2014/07/30 by Genggeng Huang, Congming Li, Huang, Genggeng +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1407.7978

arxiv created 2014/07/30 · arxiv updated 2014/07/31

Abstract

In this paper, we apply the moving plane method to the following high order degenerate elliptic equation,(-A)^p u=u^α in \mathbb Rⁿ⁺¹₊,n≥ 1,where the operator A=y∂_y²+a∂_y+Δ_x,a≥ 1. We get a Liouville theorem for subcritical case and classify the solutions for the critical case.

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