Recently, Bourgain Brezis and Mironescu proved that solutions of the stationnary Ginzburg-Landau equations in dimension 3 (and in a suitable setting) are uniformly bounded in $W^{1,p}$ for any $p < 2$. We will provide an extension and simple proof of that fact based on monotonicity arguments and on a simple (no so well known) result in harmonic analysis concerning Newtonian potentials of measures with bounded k-dimensional densities.