Quantitative Uniqueness and Vortex Degree Estimates for Solutions of the Ginzburg-Landau Equation
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In this paper, we provide a sharp upper bound for the maximal order of vanishing for non-minimizing solutions of the Ginzburg-Landau equation Δu = -1/2∊ (1 - |u|2)u which improves our previous result . An application of this result is a sharp upper bound for the degree of any vortex. We treat Dirichlet (homogeneous and non-homogeneous) as well as Neumann boundary conditions.