Calculus of Variations and Geometric Measure Theory
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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 12 Jan 2021


Accepted Paper

Inserted: 27 oct 2020
Last Updated: 12 jan 2021

Journal: COCV
Year: 2021


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


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