- Tytuł:
- Asymptotics for the minimization of a Ginzburg-Landau energy in n dimensions
- Autorzy:
- Strzelecki, Paweł
- Powiązania:
- https://bibliotekanauki.pl/articles/966865.pdf
- Data publikacji:
- 1996
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Opis:
- We prove that minimizers $u ∈ W^{1,n}$ of the functional $E_{}(u) = 1/n ∫_ |∇u|^{n} dx + 1/(4^{n}) ∫_ (1-|u|^{2})^{2} dx$, ⊂ $ℝ^{n}$, 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 $C^α_{loc}$ for any α<1 - upon passing to a subsequence $_{k} → 0$ - 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.
- Źródło:
-
Colloquium Mathematicum; 1996, 70, 2; 271-289
0010-1354 - Pojawia się w:
- Colloquium Mathematicum
- Dostawca treści:
- Biblioteka Nauki
Artykuł