Global Jacobian and Γ-convergence in a two-dimensional Ginzburg-Landau model for boundary vortices

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...

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...

Renormalized Ginzburg-Landau energy and location of near boundary vortices

We consider the location of near boundary vortices which arise in the study of minimizing sequences of Ginzburg-Landau functional with degree boundary condition. As the problem is not well-posed — minimizers do not exist, we consider a regularized problem which corresponds physically to the presence of a superconducting layer at the boundary. The study of this formulation in which minimizers no...

On compound vortices in a two-component Ginzburg-Landau functional

We study the structure of vortex solutions in a Ginzburg–Landau system for two complex valued order parameters. We consider the Dirichlet problem in the disk in R2 with symmetric, degree-one boundary condition, as well as the associated degree-one entire solutions in all of R2. Each problem has degree-one equivariant solutions with radially symmetric profile vanishing at the origin, of the same...

Dynamics of Ginzburg-Landau vortices