We study the limit p→∞ of global minimizers for a p-Ginzburg-Landau-type energy Ep(u) = ∫ δu p+1/2(1-u2)2 The minimization is carried over maps on ℝ2 that vanish at the origin and are of degree one at infinity. We prove locally uniform convergence of the minimizers on ℝ2 and obtain an explicit formula for the limit on B(0,2). Some generalizations to dimension N≥3 are presented as well.
|Original language||English (US)|
|Number of pages||16|
|Journal||Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire|
|State||Published - Jan 1 2013|
All Science Journal Classification (ASJC) codes
- Mathematical Physics
- Applied Mathematics