Uniform estimates for the parabolic Ginzburg-Landau equation
ESAIM: Control, Optimisation and Calculus of Variations, Tome 8 (2002), pp. 219-238.

We consider complex-valued solutions u ε of the Ginzburg-Landau equation on a smooth bounded simply connected domain Ω of N , N2, where ε>0 is a small parameter. We assume that the Ginzburg-Landau energy E ε (u ε ) verifies the bound (natural in the context) E ε (u ε )M 0 |logε|, 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 ε , as ε0, 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.

DOI : 10.1051/cocv:2002026
Classification : 35K55, 35J60, 58E50, 49J10
Mots clés : Ginzburg-Landau, parabolic equations, Hodge-de Rham decomposition, jacobians
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     title = {Uniform estimates for the parabolic {Ginzburg-Landau} equation},
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     pages = {219--238},
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     year = {2002},
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Bethuel, F.; Orlandi, G. Uniform estimates for the parabolic Ginzburg-Landau equation. ESAIM: Control, Optimisation and Calculus of Variations, Tome 8 (2002), pp. 219-238. doi : 10.1051/cocv:2002026. http://www.numdam.org/articles/10.1051/cocv:2002026/

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