双调和算子的基本解

Fundamental solutions for biharmonic operators

导出双调和算子△2-λ的基本解,并证明双调和算子的基本解可以由RN中含复系数的Helmholtz方程的解来表出.同时,还给出了双调和算子的基本解在无穷远点和零点处的渐进展开式.

We deduce the fundamental solutions for the biharmonic operators △2-λ. It will be shown that the fundamental solutions of biharmonic operators can be expressed in terms of the fundamental solutions of the Helmholtz equation in RN with complex coefficient. The asymptotic representation of the fundamental solutions for the biharmonic operators is given.