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Compactness results for Ginzburg-Landau type functionals with general potentials. (English) Zbl 1183.35098

Summary: We study compactness and \(\Gamma\)-convergence for Ginzburg-Landau type functionals. We only assume that the potential is continuous and positive definite close to one circular well, but allow large zero sets inside the well. We show that the relaxation of the assumptions does not change the results to leading order unless the energy is very large.

MSC:

35J20 Variational methods for second-order elliptic equations
35B25 Singular perturbations in context of PDEs
35J25 Boundary value problems for second-order elliptic equations
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