Ginzburg-Landau Vortices Paperback / softback
by Fabrice Bethuel, Haim Brezis, Frederic Helein
Part of the Progress in Nonlinear Differential Equations and Their Applications series
Paperback / softback
Description
The original motivation of this study comes from the following questions that were mentioned to one ofus by H.
Matano. Let 2 2 G= B = {x=(X1lX2) E 2; x~ + x~ = Ixl < 1}. 1 Consider the Ginzburg-Landau functional 2 2 (1) E~(u) = ~ LIVul + 4~2 L(lu1 _1)2 which is defined for maps u E H1(G;C) also identified with Hl(G;R2).
Fix the boundary condition 9(X) =X on 8G and set H; = {u E H1(G;C); u = 9 on 8G}.
It is easy to see that (2) is achieved by some u~ that is smooth and satisfies the Euler equation in G, -~u~ = :2 u~(1 _lu~12) (3) { on aGo u~ =9 Themaximum principleeasily implies (see e.g., F.
Bethuel, H. Brezisand F. Helein (2]) that any solution u~ of (3) satisfies lu~1 ~ 1 in G.
In particular, a subsequence (u~,.) converges in the w* - LOO(G) topology to a limit u*.
Information
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Item not Available
- Format:Paperback / softback
- Pages:162 pages, XXVII, 162 p.
- Publisher:Birkhauser Boston Inc
- Publication Date:28/03/1994
- Category:
- ISBN:9780817637231
Other Formats
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Information
-
Item not Available
- Format:Paperback / softback
- Pages:162 pages, XXVII, 162 p.
- Publisher:Birkhauser Boston Inc
- Publication Date:28/03/1994
- Category:
- ISBN:9780817637231
