Global minimizers for a p-Ginzburg–Landau-type energy in R2

Given ap >2, we prove existence of global minimizers for a p-Ginzburg–Landau-type energy over maps on R2 with degree d = 1 at infinity. For the analogous problem on the half-plane we prove existence of a global minimizer when p is close to 2. The key ingredient of our proof is the degree reduction argument that allows us to construct a map of degree d = 1 from an arbitrary map of degree d >1 without increasing the p-Ginzburg–Landau energy. © 2008 Elsevier Inc. All rights reserved