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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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20

Anisotropic surface energies

The surface tension energy of a liquid can be modeled, as seen in the previous chapter, by the perimeter of the region occupied by the liquid itself. Something similar happens in the study of solid crystals with sufficiently small grains, although in this case the crystalline structure of the material will lead us to observe a surface tension energy of anisotropic character. In mathematical terms, an anisotropic surface tension energy may be introduced by considering a bounded, positive Borel function Φ on S n–1 (the anisotropic surface tension) and, correspondingly, by associating with every bounded open set E with C1-boundary its Φ-surface energy,

In the isotropic case (Φ is constant), Φ-surface energy and ...

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