第一类椭圆组的第五问题

The Fifth Problem for the Elliptic Systems of PDEs of the First Kind

使用递推方法,在λ>0的情况下,解决了椭圆型方程组的第五问题解的存在唯一性.

The canonical form of elliptic systems of PDEs of the first kind is (1), the fifth problem is to seek the solutions of system (1) in the unit disc x^2 + y^2<1, such that they satisfy boundary condition (4), (5), where z = x + iy, n is the unit vector normal to the boundary |z| = 1. The existence and uniqueness of the solu- tions to the fifth problem when λ>0, which is an open question in [1,2], are obtained in this paper, the solutions are constructed explicitly.