Variational convergence for functionals of Ginzburg-Landau type

Γ-convergence of Graph Ginzburg–landau Functionals

We study Γ-convergence of graph-based Ginzburg–Landau functionals, both the limit for zero diffusive interface parameter ε → 0 and the limit for infinite nodes in the graph m→∞. For general graphs we prove that in the limit ε → 0 the graph cut objective function is recovered. We show that the continuum limit of this objective function on 4-regular graphs is related to the total variation semino...

Convergence of Ginzburg-landau Functionals in 3-d Superconductivity

In this paper we consider the asymptotic behavior of the GinzburgLandau model for superconductivity in 3-d, in various energy regimes. We rigorously derive, through an analysis via Γ-convergence, a reduced model for the vortex density, and deduce a curvature equation for the vortex lines. In the companion paper [2] we describe further applications to superconductivity and superfluidity, such as...

Compactness Results for Ginzburg-landau Type Functionals with General Potentials

We study compactness and Γ-convergence for Ginzburg-Landau type functionals. We only assume that the potential is continuous and positive definite close to one circular well, but allow large zero sets inside the well. We show that the relaxation of the assumptions does not change the results to leading order unless the energy is very large.

Lower bounds for generalized Ginzburg-Landau functionals

Γ-convergence of the Ginzburg-landau Energy

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) s...