一类具有梯度项的超定边值问题中解的对称性

The Symmetry of Solution for a Class of Overdetermined Boundary Value Problem Containing Gradient

利用经典的平行平面移动法研究一类具有梯度项的拉普拉斯方程超定问题中解的对称性,得到此类超定边值问题解和区域对称的充分条件。结果发现,解和区域的对称性依赖于非齐次项关于空间变量的连续性、对称性及关于梯度变量偏导数的连续性。

The classical moving plane method is med to investigate the symmetry of solutions for a class of Laplacian overdetermined equation which contains the gradient.The sufficient condition for the symmetry of solutions and domain is obtained and it’s found out that the symmetry of the solution and domain depends on the continuity symmetry of the non-homogeneous term on the spatial variable and the continuity on the partial derivative to the gradient.