一类半线性椭圆方程解的幂凹

Power Concavity of Solutions for a Class of Semilinear Elliptic Equations

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.