Refined Jacobian estimates for Ginzburg-Landau functionals R. JerrardDaniel Spirn 26B1035J5035Q80Ginzburg-Landau functionalJacobianGamma convergence We prove various estimates that relate the Ginzburg-Landau energy $E_{\epsilon}(u) = \int_{\Omega} |\nabla u|^2 /2 + (|u|^2 - 1)^2 /(4\epsilon^2) dx$ of a function $u \in H^1(\Omega; \mathbb{R}^2)$, $\Omega \subset \mathbb{R}^2$, to the distance in the $W^{-1,1}$ norm between the Jacobian $J(u) = \det\nabla u$ and a sum of point masses. These are interpreted as quantifying the precision with which "vortices" in a function $u$ can be located via measure-theoretic tools such as the Jacobian, and the extent to which variations in the Ginzburg-Landau energy due to translation of vortices can be detected using the Jacobian. We give examples to show that some of our estimates are close to optimal. Indiana University Mathematics Journal 2007 text pdf 10.1512/iumj.2007.56.2815 10.1512/iumj.2007.56.2815 en Indiana Univ. Math. J. 56 (2007) 135 - 186 state-of-the-art mathematics http://iumj.org/access/