环形域上的Dirichlet问题

Dirichlet Problems on the Ring Area

讨论了Laplace方程在环形域上的Dirichlet问题的求解方法,给出了该问题的求解过程和Fourier级数解的结果,并指出了Poisson积分公式在具体求解中的不适应性,对于理解S-L方程在不同边界条件下,特别是自然边界条件和周期边界条件下的本征值问题具有重要意义。

This paper discuss the solving motheds for Dirichlet problems on the ring area,give its solving process its solution form of Fourier series,this have great significance for understanding the eigen-value problems of Laplace equation on the various boundary conditions,especially on the nature boundary condition and periodic boundary condition.