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arXiv · 1401.7402

A Liouville Theorem for the Fractional Laplacian

Ran Zhuo·Wenxiong Chen·Xuewei Cui·Zixia Yuan
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Abstract

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

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Ran Zhuo, Wenxiong Chen, Xuewei Cui, Zixia Yuan. 2014-01-29. A Liouville Theorem for the Fractional Laplacian. https://arxiv.org/abs/1401.7402

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