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.