Eigenvalue problem of the Lame operator on a domain with a multi- structure

研究了由弹性体的振动特性得到的Lame算子的本征值问题。我处理的是复域它是几个薄区域的并集。当薄板趋于零时的极限系统是一个四阶ODE系统，它在顶点上具有复杂的相容条件。本文还讨论了一类低刚度系数的Lame算子的特征值问题。在具有Dirichlet条件或滑移边界条件的流体动力学问题中，得到了与Stokes算子的特征值问题有关的极限系统。

I studied the eigenvalu problem of the Lame operator, which is obtained from the oscillation property of elastic body. I dealt with the compex domain which is a union several thin regions. The limit system when the thinnes goes to zero, is a 4th order ODE system with a complicated compatibility condtions on the verticies. I also dealt with the eigenvalue problem of a certain Lame operator with the low stiffness coefficient. I obtained the limit system, which is related with the eigenvalue problem of the Stokes operator in a fluid dynamical problem with the Dirichlet condition or the slip boundary condition.