摘要
提出极小曲面问题,通过将泛函极值转化为一般函数极值的方法,将极小曲面存在惟一性问题转化为变分不等式的存在惟一性问题,得到一个重要的等价性定理.其中引入了极小曲面算子,并证明它的严格单调及半连续性,最后利用Browder-Hartman-Stampacchia变分不等式解的存在惟一性定理,得到了极小曲面的存在惟一性.
This paper first presents the problem of minimal surface. Through the method of turning a functional extremum into an extremum of general function, we transform the existence and uniqueness of minimal surface into those of variational inequality, and obtain an important equivalent theorem. We also introduce the operator of mini- mal surface and prove its strict monotonicity and semi - continuity. Finally, by using the theorem of Browder - Har- tman- Stampacchia variational inequality, the existence and uniqueness of minimal surface is proved.
出处
《菏泽学院学报》
2009年第5期20-23,共4页
Journal of Heze University
基金
河南省教育厅自然科学基金资助项目(2008C52006)
关键词
极小曲面
变分不等式
极小曲面算子
单调算子
半连续
minimal surface
variational inequality
operator of minimal surface
monotone operator
semi - continuous operator
