On a Problem Related to Vortex Nucleation of Superconductivity

In this paper we study a singularly perturbed nonlinear partial differential system which arises in the mathematical theory of superheating field of superconductivity. We prove that the maximum points of the magnitude of solutions are located near the minimum point of curvature of domain boundary. This verifies rigorously a result of Chapman obtained by formal analysis regarding the location of the vortex nucleation. We also show that the solutions exhibit boundary layers.