Fenomeni di concentrazione per energie di tipo Ginzburg-Landau

Fragalà, Ilaria

Bollettino dell'Unione Matematica Italiana, Tome 8-A (2005), p. 397-414 / Harvested from Biblioteca Digitale Italiana di Matematica

Résumé

Si discute il comportamento asintotico di energie di tipo Ginzburg-Landau, per funzioni da $\mathbb{R}^{n+k}$ in $\mathbb{R}^{k}$, e sotto l'ipotesi che l'esponente di crescita $p$ sia strettamente maggiore di $k$. In particolare, si illustra un risultato di compattezza e di $\Gamma$-convergenza, rispetto a una opportuna topologia sui Jacobiani, visti come correnti $n$-dimensionali. L'energia limite è definita sulla classe degli $n$-bordi interi $M$, e la sua densità dipende localmente dalla molteplicità di $M$ tramite una famiglia di costanti di profilo ottimale.

Abstract

We discuss the asymptotic behaviour of energies of Ginzburg-Landau type, for maps from $\mathbb{R}^{n+k}$ into $\mathbb{R}^{k}$, and when the growth exponent $p$ is strictly larger than $k$. We illustrate 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.

Détail

Publié le : 2005-06-01

MR 2149391 | Zbl 1182.49003

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