管域中Dirichlet问题的解

Solutions of the Dirichlet Problem in a Tube Domain

讨论了管状区域中Dirichlet问题解的存在性,得到了其解的积分表示.同时给出了管状区域中一类次调和函数的调和控制,证明了其就是最小的调和控制.

We discuss the existence of a solution of Dirichlet problem in a tube domain and obtain an integral representation of this solution.In the meantime,we give a harmonic majorant for a class of subharmonic functions defined in a tube domain and prove that it is the least harmonic majorant.