Γ-convergence of the Ginzburg-landau Energy
نویسنده
چکیده
From elliptic regularity one immediately has that, should such a minimizer u exist, u ∈ C∞(Ω̄). Then u is in fact a smooth (analytic, even) harmonic function obtaining the boundary value g, i.e. a solution to the classical Dirichlet problem with boundary data g. A standard exercise in the Direct Method of the Calculus of Variations provides for the existence of a minimizer, i.e. ∃u ∈ H g (Ω;R) such that E(u) = min H1 g (Ω;Rm) E (via choosing a minimizing sequence and using
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