Existence and non existence results for minimizers of the Ginzburg-Landau energy with prescribed degrees

Mickaël Dos Santos, Rémy Rodiac

Let $\mathcal{D}=\Omega \setminus \bar{\omega }\subset {\mathbb{R}}^2$ be a smooth annular type domain. We consider the simplified Ginzburg-Landau energy $E_ε(u)=\frac{1}{2}\int_{\mathcal{D}} |\n…