常均曲率方程解之唯一性 以特定邊界值出發

Abstract

我們考慮常均曲率曲面方程在某些邊界條件下的Dirichlet問題。P.Collon 得出解的存在性，他研究的是極端的例子>因此，本文涉及的是解之唯一性，也就是根據該解的存在性提供的邊界滿足某些條件下，我們最後將得出唯一性的結論。為了完成我們的工作，我們主要參考文獻[1], [2], [4]。

We consider the Dirichlet problem for the constant mean curvature surface equation on domains for some boundary data. The existence are known by P.Collon, he studied the limiting case. So this paper mainly deals with the uniqueness of the solution. That is, under the condition that the existence of solutions provided that the boundary satisfies a certain condition, we will finally give the uniqueness conclusion. To complete our work, we mainly consult [1], [2], [4].