一类分数阶椭圆型偏微分方程组解的对称性

Symmetry for solutions of a class of fractional elliptic differential system

对一类分数阶椭圆型偏微分方程组解的存在性进行了研究.采用直接移动平面法,先通过计算得到分数阶椭圆型微分方程组解的估计,推得该方程组的无穷远处衰减原理和窄区域原理,接着分三步进行证明,找到直接移动平面法所需的起点后向无穷远处移动超平面,利用反证法最终得到解的径向对称性.

We study the symmetry of solutions for a class of fractional elliptic partial differential system.In this paper,we adopt the direct method of moving planes.First,we obtain the estimation of the solutions of the system through calculation.And the decay at infinity and the narrow region principle of the system are obtained.Then,the proof is carried out in three steps.The starting point required by the direct method of moving planes is found,and then the hyperplane can be moved to infinity.The radial symmetry of the solutions is finally obtained by the direct method of moving planes and repeatedly using the proof by contradiction.