A Liouville Theorem for the Fractional Laplacian

Ran Zhuo; Wenxiong Chen; Xuewei Cui; Zixia Yuan

A Liouville Theorem for the Fractional Laplacian

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arxiv 1401.7402 v1 pith:DF45RMUM submitted 2014-01-29 math.AP

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

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keywords laplacianfractionalliouvilletheoremabovealphabelowbounded

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abstract

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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Classification of nonnegative solutions to static Schr\"{o}dinger-Hartree-Maxwell type equations
math.AP 2019-09 conditional novelty 6.0 of 10

Every nonnegative solution of the static Schrödinger-Hartree-Maxwell equations with higher-order or fractional Laplacians is either zero, or in the critical case an explicit rescaled bubble.

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