Calculus of Variations and Geometric Measure Theory

S. Baldo - G. Orlandi - S. Weitkamp

Convergence of minimizers with local energy bounds for the Ginzburg-Landau functionals.

created by orlandi on 24 Dec 2009


Published Paper

Inserted: 24 dec 2009

Journal: Indiana Univ. Math. J.
Volume: 58
Pages: 2369-2408
Year: 2009


We study the asymptotic bahaviour, as $h$ goes to 0, of a sequence $\{u_h\}$ of minimizers for the Ginzburg-Landau functional which satisfies local energy bounds of order $
\log\, h
$. The jacobians $Ju_h$ are shown to converge, in a suitable sense and up to subsequences, to an area minimizing minimal surface of codimension $2$. This is achieved without assumptions on the global energy of the sequence or on the boundary data, and holds even for unbounded domains. The proof is based on an improved version of the Gamma-convergence results from Alberti {\it et al.}, Indiana Univ. Math. J. 54 (2005), 1411--1472.

Keywords: Gamma-convergence, Local minimizers, Ginzburg-Landau