This paper examines the Laplace equation with mixed boundary conditions, the Neumann and Steklov boundary conditions. This models a container with holes in it, like a pond filled with water but partly covered by immovable pieces on the surface. The main objective is to determine the right extent of the covering pieces, so that any shock inside the container yields a resonance. To this end, an algorithm is developed which uses asymptotic formulas concerning perturbations of the partitioning of the boundary pieces. Proofs for these formulas are established. Furthermore, this paper displays some results concerning bounds and examples with regards to the governing problem.

本文研究了混合边界条件，Neumann和Steklov边界条件的Laplace方程。这样可以模拟一个带有孔的容器，就像一个装满水但部分被表面上不可移动的东西覆盖的池塘一样。主要目的是确定覆盖件的正确范围，以使容器内部的任何震动都会产生共振。为此，开发了一种算法，该算法使用关于边界块划分扰动的渐近公式。建立了这些公式的证明。此外，本文还展示了一些有关治理问题的结果和例子。