Ginzburg-Landau Vortices
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 s…
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Produktdetails
Weitere Autoren: Brezis, Haim / Helein, Frederic
- ISBN: 978-0-8176-3723-1
- EAN: 9780817637231
- Produktnummer: 1615912
- Verlag: Birkhäuser Boston
- Sprache: Englisch
- Erscheinungsjahr: 1994
- Seitenangabe: 196 S.
- Masse: H23.5 cm x B15.5 cm x D1.0 cm 306 g
- Auflage: 1994
- Abbildungen: Paperback
- Gewicht: 306
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