A Liouville Theorem for the Fractional Laplacian
By Ran Zhuo, Wenxiong CHEN *, Xuewei Cui, Zixia Yuan. 2014
58 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/4242bcde39dd4392240adef8884b328ba64080f6
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In Applied Mathematics
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In Computational Theory and Mathematics
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In Mathematical Physics
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Citations in the corpus
- On finite Morse index solutions of higher order fractional Lane-Emden equations (2014, background): “imy→0y b∂ yue = 0 in ∂R n+1 + , limy→0y b∂ y∆bue = Cn,s|u|p−1u in ∂Rn+1 + (1.7) Moreover, Z Rn |ξ|2s|u(ˆξ)|2dξ= C n,s Z Rn+1 + yb|∆ bue(x,y)|2dxdy Then u(x) = ue(x,0). For 1 <s<2, Chen et al in [6] have classified all positive solutions of (1.1) for 1 <p≤ pS(n,s). The main goal of this paper”
- Entire $s$-harmonic functions are affine (2014, background): “ville theorem holds as well and was proved by K. Bogdan et al. in [4]. Applications of Liouville theorems for nonlocal operators in the study of nonlocal elliptic systems of equations can be found in [1,8,13,14]. The aim of this paper is to classify all s-harmonic functions in RN, thereby obtaining ”