A Liouville theorem for α-harmonic functions in ℝⁿ₊

2014/09/14 by Wenxiong Chen, Congming Li, Chen, Wenxiong +5
Computer Science · Mathematics · #35J99 #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.1409.4106

openalex publication_date 2014/09/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider α-harmonic functions in the half space ℝⁿ₊: \(-Δ)^α/2 u(x)=0,~u(x) · gt;0, · amp; x∈ℝⁿ₊,
u(x)≡ 0, · amp; x∉ ℝⁿ₊.. We prove that all the solutions have to assume the form u(x)=\Cx_n^α/2, · amp; x∈ℝⁿ₊,
0, · amp; x∉ℝⁿ₊,. for some positive constant C.

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