## Abstract The author establishes the essential estimations, the __L__^__p__^ ~__loc__~ and the __C__^__α__^ estimations of |∇__u__~__ε__~ |, where __u__~__ε__~ is the minimizer of a Ginzburg–Landau type functional. Based on the results, the corresponding convergences (when __ε__ → 0) of themin
Asymptotics for the minimization of a Ginzburg-Landau functional
✍ Scribed by Fabrice Bethuel; Haim Brezis; Frédéric Hélein
- Publisher
- Springer
- Year
- 1993
- Tongue
- English
- Weight
- 871 KB
- Volume
- 1
- Category
- Article
- ISSN
- 0944-2669
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📜 SIMILAR VOLUMES
## Let be a domain in R n occupied by a superconductor material. According to the Ginzburg-Landau theory, the order parameter (complex-valued) and the induced magnetic potential A of the material must minimize the following Ginzburg-Landau functional: where H is the applied magnetic ÿeld and k is
Let W be a bounded, simply connected, regular domain of R N , N \ 2. For 0 < e < 1, let u e : W Q C be a smooth solution of the Ginzburg-Landau equation in W with Dirichlet boundary condition g e , i.e., ## ˛-Du in W, u e =g e on "W.
In this paper, the authors have studied a generalized Ginzburg᎐Landau equation Ž . in two spatial dimensions 2D . They have shown that this equation, under periodic boundary conditions, has the maximal attractor with finite Hausdorff dimension. This rigorously establishes the foundation for further