| Abstract
| - We consider complex-valued solutions u E of the Ginzburg-Landau equation on a smooth bounded simply connected domain Ω of $\mathbb{R}^N$, N ≥ 2, where ε > 0 is a small parameter. We assume that the Ginzburg-Landau energy $E_\varepsilon(u_\varepsilon)$ verifies the bound (natural in the context) $E_\varepsilon(u_\varepsilon)\le M_0|\log\varepsilon|$, where M0 is some given constant. We also make several assumptions on the boundary data. An important step in the asymptotic analysis of u E, as ε → 0, is to establish uniform L p bounds for the gradient, for some p>1. We review some recent techniques developed in the elliptic case in [7], discuss some variants, and extend the methods to the associated parabolic equation.
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