# Gamma-convergence for pattern forming systems with competing interactions

## Mercoledi 18 gennaio 2012 - Cyrill Muratov

ARGOMENTI: Seminari

SEMINARI DI EQUAZIONI DIFFERENZIALI E APPLICAZIONI
Mercoledi 18 gennaio 2012 alle ore 13:00 in aula 2BC30, Cyrill Muratov (New Jersey Institute of Technology) terra' un seminario dal titolo "Gamma-convergence for pattern forming systems with competing interactions".

-Abstract
I will discuss a problem of energy-driven pattern formation, in which the appearance of two distinct phases caused by short-range attractive forces is frustrated by a long-range repulsive force. I will focus on the regime of strong compositional asymmetry, in which one of the phases has very small volume fraction, thus creating small droplets of the minority phase in a sea of the majority phase. I will present a setting for the study of Gamma-convergence of the governing energy functional in the regime leading to many droplets. The Gamma-limit and the properties of almost minimizers with prescribed limit density will then be established in the important physical case when the long-range repulsive force is Coulombic in two space dimensions. This is joint work with D. Goldman and S. Serfaty.

Rif. int. M. Bardi, C. Marchi, M. Novaga