Geodesic
Crystalline curvature flow of planar networks
Giovanni Bellettini1 ; M. Chermisi1 ; Matteo Novaga2 orcid
1Università di Roma 'Tor Vergata', Italy
2Università di Pisa, Italy
Interfaces and free boundaries, Tome 8 (2006) no. 4, pp. 481-521

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DOI

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.
DOI : 10.4171/ifb/152
Classification : 53-XX, 74-XX, 00-XX
Mots-clés : Motion by crystalline curvature of networks, polycrystalline materials

Giovanni Bellettini  1   ; M. Chermisi  1   ; Matteo Novaga  2

1 Università di Roma 'Tor Vergata', Italy
2 Università di Pisa, Italy 
Giovanni Bellettini; M. Chermisi; Matteo Novaga. Crystalline curvature flow of planar networks. Interfaces and free boundaries, Tome 8 (2006) no. 4, pp. 481-521. doi: 10.4171/ifb/152
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