Study of a $3D$ Ginzburg-Landau functional with a discontinuous pinning term

Mickaël dos Santos (1)

1 ICJ - Institut Camille Jordan

In a convex domain $\O\subset\R^3$, we consider the minimization of a $3D$-Ginzburg-Landau type energy with a discontinuous pinning term among $H^1(\O,\C)$-maps subject to a boundary Dirichlet condition $g\in H^{1/2}(\p\O,\S^1)$. The pinning term $a:\R^3\to\R^*_+$ takes a constant value $b\in(0,1)$ in $\o$, an inner strictly convex subdomain of $\O$, and $1$ outside $\o$. We prove energy estimates with various error terms depending on assumptions on $\O,\o$ and $g$. In some special cases, we identify the vorticity lines via the concentration of the energy.

Domaines: Equations aux dérivées partielles [math.AP]

Mickaël dos Santos. Study of a $3D$ Ginzburg-Landau functional with a discontinuous pinning term. 2011. ⟨hal-00578445v1⟩