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Uniform estimates for the parabolic Ginzburg–Landau equation

F. Bethuel, G. Orlandi (2002)

ESAIM: Control, Optimisation and Calculus of Variations

We consider complex-valued solutions u ε of the Ginzburg–Landau equation on a smooth bounded simply connected domain Ω of N , N 2 , 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 | log ε | , 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 ε 0 , is to establish uniform L p bounds for the gradient, for some p > 1 . We review some recent techniques developed in...

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