Asymptotics for the minimization of a Ginzburg-Landau energy in n dimensions

Strzelecki, Paweł

Colloquium Mathematicae, Tome 70 (1996), p. 271-289 / Harvested from The Polish Digital Mathematics Library

Résumé

We prove that minimizers $u \in W^{1, n}$ of the functional $E_{} (u) = 1 / n \int_{|} {\nabla u |}^{n} d x + 1 / (4^{n}) \int_{(} 1 - {| u |}^{2})^{2} d x$ , ⊂ $ℝ^{n}$ , n ≥ 3, which satisfy the Dirichlet boundary condition $u_{} = g$ on for g: → $S^{n - 1}$ with zero topological degree, converge in $W^{1, n}$ and $C_{l o c}^{α}$ for any α<1 - upon passing to a subsequence $_{k} \to 0$ - to some minimizing n-harmonic map. This is a generalization of an earlier result obtained for n=2 by Bethuel, Brezis, and Hélein. An example of nonunique asymptotic behaviour (which cannot occur in two dimensions if deg g = 0) is presented.

Publié le : 1996-01-01

Zbl 0856.35015

EUDML-ID : urn:eudml:doc:210412

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     author = {Pawe\l\ Strzelecki},
     title = {Asymptotics for the minimization of a Ginzburg-Landau energy in n dimensions},
     journal = {Colloquium Mathematicae},
     volume = {70},
     year = {1996},
     pages = {271-289},
     zbl = {0856.35015},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv70i2p271bwm}
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Strzelecki, Paweł. Asymptotics for the minimization of a Ginzburg-Landau energy in n dimensions. Colloquium Mathematicae, Tome 70 (1996) pp. 271-289. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv70i2p271bwm/

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