高阶复偏微分方程的Rubin问题

Rubin problems of higher order complex partial differential equations

利用复平面上Cauchy型奇异积分算子的性质,在一阶Dirichlet边值问题的基础上,讨论了单位圆盘上解析函数的Rubin问题,并在此基础上研究了关于高阶复偏微分方程的Rubin问题,从而得到其解的积分表示和相应的可解条件.

By the properties of Cauchy type singular integral operators in the complex plain,on the basis of lower order Dirichlet boundary value problems,the Rubin problem for analytic functions on the unit disc is discussed.Then the Rubin problem about higher order complex partial differential equations is studied and the integral representation of the solution and the solvable condition are given.