Fenomeni di concentrazione per energie di tipo Ginzburg-Landau

Fragalà, Ilaria

Bollettino della Unione matematica italiana, Série 8, 8B (2005) no. 2, pp. 397-414

Résumé

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.