Calculus of Variations and Geometric Measure Theory

A. Braides - V. Vallocchia

Two geometric lemmas for $S^{N-1}$-valued maps and an application to the homogenization of spin systems

created by braidesa on 27 Oct 2020
modified on 03 Sep 2021


Published Paper

Inserted: 27 oct 2020
Last Updated: 3 sep 2021

Journal: COCV
Volume: 27
Pages: 13
Year: 2020
Doi: 10.1051/cocv/2021007


We prove two geometric lemmas for $S^{N-1}$-valued functions that allow to modify sequences of lattice spin functions on a small percentage of nodes during a discrete-to-continuum process so as to have a fixed average. This is used to simplify known formulas for the homogenization of spin systems.

Keywords: Homogenization, discrete systems, spin systems, lattice energies, discrete-to-continuum, Liquid crystals