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

Given a p > 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.