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投稿时间：2015-09-02
投稿时间：2015-09-02
中文摘要: 研究了一类半线性椭圆方程解的几何性质.通过构造粘性凹包络，以及利用粘性解的性质，得出了半线性椭圆方程解的幂函数是凹函数的结论.并利用方程的解和其水平集之间的关系，证明了解的水平集是凸集.
Abstract:Geometric properties of solutions are investigated for a class of semilinear elliptic equations.Firstly,by constructing viscosity concave envelope and using properties of viscosity solution,power concavity is obtained for the solutions of semilinear elliptic equations.Then,taking advantage of the relationship between the solutions of equations and their level sets,convexity of the level sets is proved.
文章编号：201600520 中图分类号： 文献标志码：
基金项目:
| 作者 | 单位 | |
| 李丽花 | 上海电力学院 数理学院 | dlxyllh2004@163.com |
| Author Name | Affiliation | |
| LI Lihua | School of Mathematics and Physics, Shanghai University of Electric Power, Shanghai 200090, China | dlxyllh2004@163.com |
引用文本：
李丽花.一类半线性椭圆方程解的幂凹[J].上海电力大学学报,2016,32(5):507-509.
LI Lihua.Power Concavity of Solutions for a Class of Semilinear Elliptic Equations[J].Journal of Shanghai University of Electric Power,2016,32(5):507-509.
李丽花.一类半线性椭圆方程解的幂凹[J].上海电力大学学报,2016,32(5):507-509.
LI Lihua.Power Concavity of Solutions for a Class of Semilinear Elliptic Equations[J].Journal of Shanghai University of Electric Power,2016,32(5):507-509.