Calculus of Variations and Geometric Measure Theory

A. Braides

Discrete-to-Continuum Variational Methods for Lattice Systems

created by braidesa on 26 Sep 2014



Inserted: 26 sep 2014
Last Updated: 26 sep 2014

Journal: International Congress of Mathematicians (ICM 2014), Seoul, 2014
Year: 2014


I review some recent results regarding the description of the behaviour of energy-driven discrete systems, and more precisely lattice systems, through the construction of approximate continuous problems. On one hand methods of weak convergence, homogenization, integral representation and gradient ow dynamics already used for continuum problems have been adapted to the discrete setting, on the other hand the new discrete dimension has brought new phenomena, novel problems and interesting results. I will limit my description to systems with interfacial energies, but focus on methods that can be adapted to a multi-scale analysis.