A Liouville Theorem for the Fractional Laplacian

Ran Zhuo; Wenxiong Chen; Xuewei Cui; Zixia Yuan

arxiv: 1401.7402 · v1 · pith:DF45RMUMnew · submitted 2014-01-29 · 🧮 math.AP

A Liouville Theorem for the Fractional Laplacian

Ran Zhuo , Wenxiong Chen , Xuewei Cui , Zixia Yuan This is my paper

classification 🧮 math.AP

keywords laplacianfractionalliouvilletheoremabovealphabelowbounded

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We extend the classical Liouville Theorem from Laplacian to the fractional Laplacian, that is, we prove Every $\alpha$-harmonic function bounded either above or below in all of $R^n$ must be constant.

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A Liouville Theorem for the Fractional Laplacian

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