調和函數的推廣

Abstract

這篇文章主要是由F. Reese Harvey及H. Blaine Lawson, Jr.所寫的文章(參考文獻[2])中推廣調和函數的定義，並且說明存在性以及唯一性之間的關係、等價條件等。而這些證明及等價關係是由F. Reese Harvey及H. Blaine Lawson, Jr.所寫的文章(參考文獻[1])中所提出以及證明，而這篇文章中將細節敘述的更加完整，使得文章容易閱讀。

In [2]Dirichlet duality and the nonlinear Dirichlet problem, the Dirichlet problem of equation(or Dirichlet set) was discussed about its existence and uniqueness. About its existence, the paper uses Perron Solution to prove it. The solution likes a classical Perron method for existence of solution to Dirichlet problem on R^n ball. In this paper, it extends the definition for equation about two subequations E and G. And then we discuss its existence, uniqueness and some properties. Basically, this article is reported on a published paper, see[1].