Calculus of Variations and Geometric Measure Theory

R. Alicandro - G. Lazzaroni - M. Palombaro

On the effect of interactions beyond nearest neighbours on non-convex lattice systems

created by lazzaroni on 30 Nov 2016
modified on 23 Mar 2017


Published Paper

Inserted: 30 nov 2016
Last Updated: 23 mar 2017

Journal: Calc. Var. Partial Differential Equations
Volume: 56:42
Year: 2017
Doi: 10.1007/s00526-017-1129-5


We analyse the rigidity of non-convex discrete energies where at least nearest and next-to-nearest neighbour interactions are taken into account. Our purpose is to show that interactions beyond nearest neighbours have the role of penalising changes of orientation and, to some extent, they may replace the positive-determinant constraint that is usually required when only nearest neighbours are accounted for. In a discrete to continuum setting, we prove a compactness result for a family of surface-scaled energies and we give bounds on its possible Gamma-limit in terms of interfacial energies that penalise changes of orientation.