一类半空间上分数阶Laplace方程的Liouville定理

Liouville Type Theorem for a Fractional Laplacian in a Half Space

首先研究了半空间上一类满足Dirichlet边值问题的分数阶Laplace方程与其对应的积分方程解的等价性;然后,基于两个方程解的等价性,运用积分形式的移动平面法证明了积分方程在全局可积条件下的正解的不存在性以及其在局部有界的条件下的Liouville型定理.

This paper investigates the Liouville type theorem of a fractional laplacian in a half space. Firstly,we show the equivalence between the differential equation and the integral equation. Based on the equivalence,we use the moving plane meth- od in integral equation to establish the non-existence of positive solutions under the Global Integrability Assumption and a Li- ouville type theorem with Weaker Conditions.