{"product_id":"ginzburg-landau-vortices-von-fabrice-bethuel-haim-brezis-frederic-helein","title":"Ginzburg-Landau Vortices","description":"\u003cp\u003eThe 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 \u0026lt; 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*.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9780817637231\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9780817637231","offer_id":39415343644765,"sku":"9780817637231","price":106.99,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/a09ad77c-66e9-4b92-9ec6-47a50591e735.jpg?v=1772168516","url":"https:\/\/shop.autorenwelt.de\/products\/ginzburg-landau-vortices-von-fabrice-bethuel-haim-brezis-frederic-helein","provider":"Autorenwelt Shop","version":"1.0","type":"link"}