Convergence of the parabolic Ginzburg–Landau equation to motion by mean curvature

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A second derivative Hölder estimate for weak mean curvature flow (2012, background): “Numerous works which have even more direct relations to Brakke’s MCF are singular perturbation limit problems such as the Allen-Cahn equation [11, 15] and the parabolic Ginzburg-Landau equation [3, 4, 12, 14].”
A general regularity theory for weak mean curvature flow (2011, methodology): “We are unaware of any general method in case k < n− 1, most relevant being the approximation scheme via the parabolic GinzburgLandau equation [6] where u = 0, k = n− 2 and n ≥ 3.”
Gamma-convergence of gradient flows on Hilbert and metric spaces and applications (2011, background): “In some cases one can succeed in getting around them or solving them, as done for example in [20, 6, 35, 50, 41].”