A remark on the radial minimizer of the Ginzburg-Landau functional

الأصل · EN

Denote by Eε the Ginzburg-Landau functional in the plane and let uε be the radial solution to the Euler equation associated to the problem {Eε(u,B₁):. u ∂ B₁=(ϑ, ϑ)}. Let Ω⊂ ² be a smooth, bounded domain with the same area as B₁. Denoted by K={v=(v₁,v₂) ∈ H¹(Ω;²): ∫Ωv₁dx=∫Ωv₂dx=0, ∫Ω|v|²dx≥ ∫B₁ | uε|²dx}, we prove ᵥ ∈ ₖ Eε (v,Ω)≤ Eε (uε,B₁).