We continue our study of the functional for u ε H1 (U; ℝ2), where U is a bounded, open subset of ℝ2. Compactness results for the scaled Jacobian of ue are proved under the assumption that Ee(ue) is bounded uniformly by a function of e. In addition, the Gamma limit of Ee(ue)/(ln e)2 is shown to be where v is the limit of j(ue)/ ln e , j(ue) := ue x Due, and ∥ · ∥ is the total variation of a Radon measure. These results are applied to the Ginzburg-Landau functional with external magnetic field hext ≈ H ln e . The Gamma limit of Fe/(ln e)2 is calculated to be where v is as before, and a is the limit of Ae/ ln e .
All Science Journal Classification (ASJC) codes
- Gamma limit
- Ginzburg-Landau functional