Calculus of Variations and Geometric Measure Theory

G. Bellettini - M. Chermisi - M. Novaga

Crystalline curvature flow of planar networks

created by novaga on 20 Jan 2006
modified by chermisi on 15 Apr 2010


Published Paper

Inserted: 20 jan 2006
Last Updated: 15 apr 2010

Journal: Interfaces Free Bound.
Year: 2006


We consider the evolution of a polycrystalline material with three or more phases, in presence of an even crystalline anisotropy. We analyze existence, uniqueness, regularity and stability of the flow. In particular, if the flow becomes unstable at a finite time, we prove that an additional segment (or even an arc) at the triple junction may develop in order to decrease the energy and make the flow stable at subsequent times. We discuss some examples of collapsing situations that lead to changes of topology, such as the collision of two triple junctions.