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

PHYSICA D-NONLINEAR PHENOMENA

卷:419

Article

Dipierro, Serena¹  Poggesi, Giorgio¹  Valdinoci, Enrico¹ 

[1] Univ Western Australia, Dept Math & Stat, 35 Stirling Highway, Perth, WA 6009, Australia

关键词: Lattice systems;    Crystals;    Equilibrium configurations;    Rigidity results;    PDE methods;   

DOI  :  10.1016/j.physd.2021.132871

来源: Elsevier

【 摘 要 】

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 these types of methodologies inspired by continuum models. (C) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

Free