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Eigenvalue problems of Ginzburg-Landau operator in bounded domains. (English) Zbl 0943.35058
Summary: We study eigenvalue problems for the Ginzburg-Landau operator with a large parameter on bounded domains in \(\mathbb{R}^2\) under gauge invariant boundary conditions. The estimates for the eigenvalues are obtained and the asymptotic behavior of the associated eigenfunction are dicussed. These results play a key role in estimating the critical magnetic field in the mathematical theory of superconductivity.

MSC:
35P15 Estimates of eigenvalues in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
58E99 Variational problems in infinite-dimensional spaces
35Q60 PDEs in connection with optics and electromagnetic theory
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