In questo lavoro si studia una classe di funzionali che intervengono in molti problemi di Fisica Matematica e, in particolare, nel problema di trovare le configurazioni di equilibrio di una miscela di liquidi isotropi e cristalli liquidi.

Les équations bidimensionnelles d'une coque non linéairement élastique «en flexion» ont été récemment justifiées par V. Lods et B. Miara par la méthode des développements asymptotiques formels appliquée aux équations de l'élasticité non linéaire tridimensionnelle. Ces équations se mettent sous la forme d'un problème de point critique d'une fonctionnelle dont l'intégrande est une expression quadratique en termes de la différence exacte entre les tenseurs de courbure des surfaces déformée et non déformée,...

We consider complex-valued solutions $u_{\epsilon }$ of the Ginzburg–Landau equation on a smooth bounded simply connected domain $\Omega$ of ${ℝ}^N$, $N\ge 2$, where $\epsilon \>0$ is a small parameter. We assume that the Ginzburg–Landau energy $E_{\epsilon }\left(u_{\epsilon }\right)$ verifies the bound (natural in the context) $E_{\epsilon }\left(u_{\epsilon }\right)\le M_0|log\epsilon |$, where $M_0$ is some given constant. We also make several assumptions on the boundary data. An important step in the asymptotic analysis of $u_{\epsilon }$, as $\epsilon \to 0$, is to establish uniform $L^p$ bounds for the gradient, for some $p\>1$. We review some recent techniques developed in...

We consider complex-valued solutions uE of the Ginzburg–Landau equation on a smooth bounded simply connected domain Ω of ${ℝ}^N$, N ≥ 2, where ε > 0 is a small parameter. We assume that the Ginzburg–Landau energy $E_{\epsilon }\left(u_{\epsilon }\right)$ verifies the bound (natural in the context) $E_{\epsilon }\left(u_{\epsilon }\right)\le M_0|log\epsilon |$, where M0 is some given constant. We also make several assumptions on the boundary data. An important step in the asymptotic analysis of uE, as ε → 0, is to establish uniform Lp bounds for the gradient, for some p>1. We review some...