Variational convergence for functionals of Ginzburg-Landau type

In the first part of this paper we prove that functionals of Ginzburg-Landau type for maps from a domain in dimension n+k into 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 the paper "Un risultato di convergenza variazionale per funzionali di tipo Ginzburg-Landau in dimensione qualunque" by the first author.