Calculus of Variations and Geometric Measure Theory

R. Alicandro - N. Ansini

A variational model of interaction between continuum and discrete systems

created by alicandr on 03 Aug 2012
modified by ansini on 09 Sep 2014


Published Paper

Inserted: 3 aug 2012
Last Updated: 9 sep 2014

Journal: Math. Mod. Meth. Appl. Sci. (M3AS)
Volume: 24
Pages: 1957-2008
Year: 2014


We consider a variational model which describes a complex system composed, in its reference con guration, of a periodic distribution of `small' interacting particles immersed in a continuous medium. We describe its macroscopic limit via Gamma-convergence, highlighting different regimes. In particular, we show how the interplay between the particles and the continuum leads, for a critical size of the particles, to a capacitary term. Eventually, we discuss how the presence of a continuum aff ects the properties of the ground states of the system of particles in terms of the validity or not of the so called `Cauchy-Born' rule.