Journal
INDIANA UNIVERSITY MATHEMATICS JOURNAL
Volume 54, Issue 5, Pages 1411-1472Publisher
INDIANA UNIV MATH JOURNAL
DOI: 10.1512/iumj.2005.54.2601
Keywords
Ginzburg-Landau functional; jacobians; integral currents; flat convergence and compactness; Gamma-convergence; minimal surfaces
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In the first part of this paper we prove that certain functionals of Ginzburg-Landau type for maps from a domain in Rn+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 [2].
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