A quantitative rigidity result for a two-dimensional Frenkel-Kontorova model
Analysis of PDEs
2021-03-17 v1
Abstract
We consider a Frenkel-Kontorova system of harmonic oscillators in a two-dimensional Euclidean lattice and we obtain a quantitative estimate on the angular function of the equilibria. The proof relies on a PDE method related to a classical conjecture by E. De Giorgi, also in view of an elegant technique based on complex variables that was introduced by A. Farina. In the discrete setting, a careful analysis of the reminders is needed to exploit this type of methodologies inspired by continuum models.
Cite
@article{arxiv.2102.04630,
title = {A quantitative rigidity result for a two-dimensional Frenkel-Kontorova model},
author = {Serena Dipierro and Giorgio Poggesi and Enrico Valdinoci},
journal= {arXiv preprint arXiv:2102.04630},
year = {2021}
}