# Concentration of Ginzburg-Landau energies with supercritical'' growth

created on 29 Jul 2003
modified by fragala on 14 Dec 2006

[BibTeX]

Published Paper

Inserted: 29 jul 2003
Last Updated: 14 dec 2006

Journal: SIAM Journal of Mathematical Analysis
Volume: 38
Pages: 385-413
Year: 2006

Abstract:

\font\filt=msbm10 \def \rek {\hbox{\filt R} k} \def \renk {\hbox{\filt R} {n+k}}

We study the asymptotic behaviour of energies of Ginzburg-Landau type, for maps from $\renk$ into $\rek$, and when the growth exponent $p$ is strictly larger than $k$. We prove a compactness and $\Gamma$-convergence result, with respect to a suitable topology on the Jacobians, seen as $n$-dimensional currents. The limit energy is defined on the class of $n$-integral boundaries $M$, and its density depends locally on the multiplicity of $M$ through a family of optimal profile constants.

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