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We consider minimizers of the energy Eε(u)=:∫Ω[1/2|■u|^2+1/4ε2(|u|^2-1)^2]dx+1/2ε^s∫■ΩW(u,g)ds,u:Ω→■,0<s<1,in a two-dimensional domain W,with weak anchoring potential W(u,g)=:1/2(|u|^2-1)^2+(<u,g>-cosα)^2,0<a<π/2.This functional was prev