Sergio Conti, Adriana Garroni, Annalisa Massaccesi
Published 2014-09-22Version 1
In the modeling of dislocations one is lead naturally to energies concentrated on lines, where the integrand depends on the orientation and on the Burgers vector of the dislocation, which belongs to a discrete lattice. The dislocations may be identified with divergence-free matrix-valued measures supported on curves or with 1-currents with multiplicity in a lattice. In this paper we develop the theory of relaxation for these energies and provide one physically motivated example in which the relaxation for some Burgers vectors is nontrivial and can be determined explicitly. From a technical viewpoint the key ingredients are an approximation and a structure theorem for 1-currents with multiplicity in a lattice.
Integral representation for functionals defined on $SBD^p$ in dimension two
On the regularity of the $ω$-minima of $\varphi$-functionals
Approximation and relaxation of perimeter in the Wiener space
![QR code for arXiv:1409.6084 [math.AP]](http://oss.arxitics.com/images/favicon.svg)