We introduce and study certain variants of Gamow’s liquid drop model in which an anisotropic surface energy replaces the perimeter. After existence and nonexistence results are established, the shape of minimizers is analyzed. Under suitable regularity and ellipticity assumptions on the surface tension, Wulff shapes are minimizers in this problem if and only if the surface energy is isotropic. In sharp contrast, Wulff shapes are the unique minimizers for certain crystalline surface tensions. We also introduce and study several related liquid drop models with anisotropic repulsion for which the Wulff shape is the minimizer in the small mass regime.

中文翻译：

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各向异性液滴模型

我们介绍并研究了 Gamow 液滴模型的某些变体，其中各向异性表面能取代了周长。确定存在和不存在结果后，分析极小值的形状。在表面张力的适当规则性和椭圆率假设下，当且仅当表面能是各向同性的时，Wulff 形状在这个问题中是最小的。形成鲜明对比的是，Wulff 形状是某些晶体表面张力的独特最小化剂。我们还介绍和研究了几个相关的具有各向异性排斥力的液滴模型，其中 Wulff 形状是小质量状态下的最小值。