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arXiv · 2102.04630

A quantitative rigidity result for a two-dimensional Frenkel-Kontorova model

Serena Dipierro·Giorgio Poggesi·Enrico Valdinoci
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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.

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Serena Dipierro, Giorgio Poggesi, Enrico Valdinoci. 2021-02-09. A quantitative rigidity result for a two-dimensional Frenkel-Kontorova model. https://doi.org/10.1016/j.physd.2021.132871

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