We consider the physical configuration of a container which holds a finite number of movable solid objects and three immiscible fluids. Each fluid volume is prescribed, and the container is completely filled. The configuration is modeled using sets of finite perimeter, and the energy of the configuration is given using the theory of functions of bounded variation. We show that there exists an admissible configuration that attains the minimum energy.

中文翻译：

---

漂浮在三种液体浴中的多个固体物体的能量最小化配置的存在

我们考虑一个容纳有限数量的可移动固体和三种不混溶流体的容器的物理构造。规定了每个液体的体积，然后将容器完全充满。使用有限周长集对配置进行建模，并使用有界变化函数的理论给出配置的能量。我们证明了存在一种可以达到最小能量的构型。