一类半空间上分数阶Laplace方程的Liouville定理 |
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作者单位: | ;1.河南师范大学数学与信息科学学院 |
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摘 要: | 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.
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关 键 词: | 格林函数 积分方程的移动平面法 不存在性 Liouville型定理 |
Liouville Type Theorem for a Fractional Laplacian in a Half Space |
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Affiliation: | ,College of Mathematics and Information Science,Henan Normal University |
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Abstract: | 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 method in integral equation to establish the non-existence of positive solutions under the Global Integrability Assumption and a Liouville type theorem with Weaker Conditions. |
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Keywords: | Green's function moving plane method in integral equation non-existence Liouville type theorem |
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