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Sets of Finite Perimeter and Geometric Variational Problems: An Introduction to Geometric Measure Theory by Francesco Maggi

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19

Equilibrium shapes of liquids and sessile drops

In this chapter we study the equilibrium shapes of a liquid confined in a given container, with particular emphasis on the model problem of the sessile liquid drop. This is a classical subject, with a huge interdisciplinary literature. Therefore we shall provide here only a rough introduction to this theory, referring the reader to the beautiful book [Fin86] for a more complete account. At the same time, the study of these problems will allow us to provide significant and instructive applications of the various methods and ideas developed so far. Since the work of Gauss, the problem is studied through the introduction of a free energy functional. Precisely, if a liquid occupies a region E

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