Calculus of Variations and Geometric Measure Theory

R. Choksi - R. Neumayer - I. Topaloglu

Anisotropic liquid drop models

created by topaloglu1 on 03 Aug 2019



Inserted: 3 aug 2019

Year: 2018

ArXiv: 1810.08304 PDF


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.