Title: Variational convergence for functionals of Ginzburg-Landau type

Authors: Giovanni Alberti, Sisto Baldo and Giandomenico Orlandi

Issue: Volume 54 (2005), Issue 5, 1411-1472

Abstract: In the first part of this paper we prove that functionals of Ginzburg-Landau type for maps from a domain in $\mathbb{R}^{n+k}$ into $\mathbb{R}^k$ converge in a suitable sense to the area functional for surfaces of dimension $n$ (Theorem 1.1). In the second part we modify this result in order to include Dirichlet boundary condition (Theorem 5.5), and, as a corollary, we show that the rescaled energy densities and the Jacobians of minimizers converge to minimal surfaces of dimension $n$ (Corollaries 1.2 and 5.6). Some of these results were announced in: Giovanni Alberti, "Variational models for phase transitions, an approach via $\Gamma$-convergence," in "Calculus of Variations and Partial Differential Equations (Pisa, 1996)," edited by G. Butazzo et al. (Springer, Berlin, 2000), pp. 95--114.