Calculus of Variations and Geometric Measure Theory

E. Mainini - P. Piovano - U. Stefanelli

Crystalline and isoperimetric square configurations

created by piovano on 28 Aug 2016
modified on 30 Aug 2016



Inserted: 28 aug 2016
Last Updated: 30 aug 2016

Year: 2014


We present crystallization results for planar atomic interactions governed by two- and three-body terms with the resulting periodicity being that of the square lattice. The emergence of a (square) Wulff shape for ground states is established by showing the optimality of ground-state configurations in terms of a discrete isoperimetric inequality. Furthermore, an $n^{3/4}$ law for the deviation from the asymptotic Wulff shape is established with an explicit constant for the leading term.