Ginzburg-Landau Vortices

di Fabrice Bethuel (Autore)

Haim Brezis (Autore)

Frederic Helein (Autore)

Birkhauser Boston Inc, 1994

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*.

• Autore: Fabrice Bethuel, Haim Brezis, Frederic Helein
• Editore: Birkhauser Boston Inc
• Collana: Progress in Nonlinear Differential Equations and Their Applications
• Anno: 1994
• Rilegatura: Paperback / softback
• Pagine: 162 p.
• Dimensioni: 235 x 155 mm
• EAN: 9780817637231

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