Pinning of Vortices for a Variational Problem Related to the Superconducting Thin Films Having Variable Thickness

Abstract

This paper is concerned with the minimization problem related to the superconducting thin films having variable thickness. The asymptotic behavior of the minimizers is discussed. The singularities are found to be located at the thinnest positions of the film and the vortices of u_ε are proved to be pinned near these regions.