一类半线性椭圆方程解的幂凹  

Power Concavity of Solutions for a Class of Semilinear Elliptic Equations

作　　者：李丽花[1] 

机构地区：[1]上海电力学院数理学院,上海200090

出　　处：《上海电力学院学报》2016年第5期507-509,共3页Journal of Shanghai University of Electric Power

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.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.

关 键 词：半线性椭圆方程 幂凹 水平集 

分 类 号：O175.25[理学—数学]