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Liouville-type theorems for a system of fractional Laplacian equations
Complex Variables and Elliptic Equations ( IF 0.9 ) Pub Date : 2021-07-01 , DOI: 10.1080/17476933.2021.1945586
Rong Yin 1 , Jihui Zhang 2 , Xudong Shang 3
Affiliation  

In the paper, we study the following system of partial differential equations (PDEs) involving fractional Laplacian operators (1) ()α2u=vq,xR+n,()β2v=up,xR+n,(1) under the boundary conditions u0, v0, xRnR+n, where p(1,n+βnα], q(1,n+αnβ], 0<α, β<2 and n3. In order to overcome the difficulty that there are no corresponding maximum principles for the operators ()α2 and ()β2 in R+n, we employ the method of moving planes in integral forms to the system of integral equations which is equivalent to System (1). Then, we obtain some Liouville type theorems for a pair of solutions (u,v) of System (1) under different assumptions.



中文翻译:

分数拉普拉斯方程系统的刘维尔型定理

在本文中,我们研究了以下涉及分数拉普拉斯算子的偏微分方程 (PDE) 系统(1)(-)α2=vq,XR+n,(-)β2v=p,XR+n,(1)边界条件下0, v0, XRnR+n, 在哪里p(1,n+βn-α],q(1,n+αn-β],0<α, β<2n3. 为了克服算子没有对应的最大值原则的困难(-)α2(-)β2R+n,我们采用积分形式的平面移动方法到积分方程组,相当于系统(1)。然后,我们得到一些关于一对解的刘维尔型定理(,v)系统(1)在不同的假设下。

更新日期:2021-07-01
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