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.