APPROXIMATIONS WITH VORTICITY BOUNDS FOR THE GINZBURG–LANDAU FUNCTIONAL

We propose an approximation scheme for complex-valued functions defined on a smooth domain Ω: the approximating functions have a Ginzburg–Landau energy of the same magnitude as the initial function, but they possess moreover improved bounds on vorticity. As an application, we obtain a variant of a Jacobian estimate first established by Jerrard and Soner. This variant was conjectured by Bourgain, Brezis and Mironescu.

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