下调和函数的性质与判定研究

Study on Properties and Determination Methods of Subharmonic Functions

调和函数是偏微分方程理论研究中的一类重要函数,特别是在椭圆型偏微分方程理论研究中的地位非常重要。下调和函数是调和函数的一个推广。对下调和函数作了深入研究,运用数学分析方法和技巧,给出并证明了下调和函数的两个重要性质和两个判定方法。

Harmonic functions are essential in the theoretical research of partial differential equations,especially in elliptic partial differential equations.The subharmonic function is a generalization of the harmonic function.In this paper,we make a deep study of subharmonic functions.Furthermore,we give and prove two critical properties and two determination methods of subharmonic functions.