Singular lines in liquid crystals. (English) Zbl 0731.49038

Differential equations and their applications, Proc. 7th Conf., Equadiff 7, Prague/Czech. 1989, Teubner-Texte Math. 118, 202-203 (1990).
[For the entire collection see Zbl 0704.00019.]
This paper reports on results presented in detail elsewhere. These results concern the treatment of the relaxed energy of liquid crystals in terms of Cartesian currents, in comparison with the Sobolev space setting.
The class of currents in \({\mathbb{R}}^ 3\times {\mathbb{S}}^ 2\) which is considered consists of those 3-dimensional currents of the form \(T=[[G_{u_ T}]]+L_ T\times [[{\mathbb{S}}^ 2]]\) which are supported in \({\bar \Omega}\times {\mathbb{S}}^ 2\) and satisfy \(\partial T=[[G_{\phi}]]\). \((G_ f\) denotes the graph of f, and \(\phi\) is a function on Bdry(\(\Omega\)).) The energy functional which is considered is \[ \int | Du_ T|^ 2 dx+4\pi M_{\Omega}(L_ T). \]


49Q20 Variational problems in a geometric measure-theoretic setting


Zbl 0704.00019