Uniform estimates for the parabolic Ginzburg-Landau equation
ESAIM: Control, Optimisation and Calculus of Variations, Volume 8 (2002), p. 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 : https://doi.org/10.1051/cocv:2002026
Classification:  35K55,  35J60,  58E50,  49J10
Keywords: Ginzburg-Landau, parabolic equations, Hodge-de Rham decomposition, jacobians
@article{COCV_2002__8__219_0,
     author = {B\'ethuel, Fabrice and Orlandi, G.},
     title = {Uniform estimates for the parabolic Ginzburg-Landau equation},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     publisher = {EDP-Sciences},
     volume = {8},
     year = {2002},
     pages = {219-238},
     doi = {10.1051/cocv:2002026},
     zbl = {1078.35013},
     language = {en},
     url = {http://www.numdam.org/item/COCV_2002__8__219_0}
}
Bethuel, F.; Orlandi, G. Uniform estimates for the parabolic Ginzburg-Landau equation. ESAIM: Control, Optimisation and Calculus of Variations, Volume 8 (2002) pp. 219-238. doi : 10.1051/cocv:2002026. http://www.numdam.org/item/COCV_2002__8__219_0/

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