Uniqueness of vortexless Ginzburg-Landau type minimizers in two dimensions
نویسندگان
چکیده
In a simply connected two dimensional domain Ω, we consider Ginzburg-Landau minimizers u with zero degree Dirichlet boundary condition g ∈ H1/2(∂Ω;S1). We prove uniqueness of u whenever either the energy or the Ginzburg-Landau parameter are small. This generalizes a result of Ye and Zhou requiring smoothness of g. We also obtain uniqueness when Ω is multiply connected and the degrees of the vortexless minimizer u are prescribed on the components of the boundary, generalizing a result of Golovaty and Berlyand for annular domains. The proofs rely on new global estimates connecting the variation of |u| to the Ginzburg-Landau energy of u. These estimates replace the usual global pointwise estimates satisfied by ∇u when g is smooth, and apply to fairly general potentials. In a related direction, we establish new uniqueness results for critical points of the Ginzburg-Landau energy.
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