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

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.