Troy: The existence of multiple solu- tions for a Ginzburg-Landau type model of superconductivity
- S. P. Hastings, W.C.M.K. Kwong
In continuation with our preceding paper 3] concerning the su-perconducting lm, we present in this article new estimates for the superheating eld in the weak limit. The principal result is the proof of the existence of a nite superheating eld h sh;+ () (obtained by restricting the usual deenition of the superheating eld to solutions of the Ginzburg-Landau system (f; A) with f positive) in the case of a semi-innnite interval. The bound is optimal in the limit ! 0 and permits to prove (combining with our previous results) the De Gennes formula 2 ? 3 4 = lim !0 1 2 h sh;+ () 1 The proof is obtained by improving slightly the estimates given in 3] where an upper bound was found but under the additional condition that the function f was bounded from below by some xed constant > 0.