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Displaying similar documents to “Local minimizers with vortex filaments for a Gross-Pitaevsky functional”

Magnetic vortices for a Ginzburg-Landau type energy with discontinuous constraint

Ayman Kachmar (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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This paper is devoted to an analysis of vortex-nucleation for a Ginzburg-Landau functional with discontinuous constraint. This functional has been proposed as a model for vortex-pinning, and usually accounts for the energy resulting from the interface of two superconductors. The critical applied magnetic field for vortex nucleation is estimated in the London singular limit, and as a by-product, results concerning vortex-pinning and boundary conditions on the interface are obtained. ...

Critical points of Ambrosio-Tortorelli converge to critical points of Mumford-Shah in the one-dimensional Dirichlet case

Gilles A. Francfort, Nam Q. Le, Sylvia Serfaty (2009)

ESAIM: Control, Optimisation and Calculus of Variations

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Critical points of a variant of the Ambrosio-Tortorelli functional, for which non-zero Dirichlet boundary conditions replace the fidelity term, are investigated. They are shown to converge to particular critical points of the corresponding variant of the Mumford-Shah functional; those exhibit many symmetries. That Dirichlet variant is the natural functional when addressing a problem of brittle fracture in an elastic material.

Γ-convergence approach to variational problems in perforated domains with Fourier boundary conditions

Valeria Chiadò Piat, Andrey Piatnitski (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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The work focuses on the Γ-convergence problem and the convergence of minimizers for a functional defined in a periodic perforated medium and combining the bulk (volume distributed) energy and the surface energy distributed on the perforation boundary. It is assumed that the mean value of surface energy at each level set of test function is equal to zero. Under natural coercivity and -growth assumptions on the bulk energy, and the assumption that the surface energy satisfies -growth...