Two geometric lemmas for SN-1-valued maps and an application to the homogenization of spin systems

Andrea Braides, Valerio Vallocchia
2021 E S A I M: Control, Optimisation and Calculus of Variations  
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.
doi:10.1051/cocv/2021007 fatcat:qvlccexmj5eibemjsr2yos4ld4