A Solid Object Floating in a Bath of Three Fluids
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We consider a bounded container filled by three immiscible fluids and a solid object, presumably floating at one or more of the interfaces. Fluids are modeled by Caccioppoli sets. The energy in our model is assumed to come from gravity, adhesion energy, and surface tension. We shall use the theory of functions of bounded variation to show that the energy functional attains a minimum for some configurations of the fluids and solid.