APPROXIMATIONS WITH VORTICITY BOUNDS FOR THE GINZBURG–LANDAU FUNCTIONAL

DOI10.1142/S0219199704001537zbMath1129.35329OpenAlexW2157676086MaRDI QIDQ4675807

Didier Smets, Giandomenico Orlandi, Fabrice Bethuel

Publication date: 6 May 2005

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219199704001537

Mathematics Subject Classification ID

Variational methods involving nonlinear operators (47J30) Singular perturbations in context of PDEs (35B25) Variational methods for second-order elliptic equations (35J20) Applications of functional analysis to differential and integral equations (46N20)

Related Items (18)

New estimates for the Laplacian, the div-curl, and related Hodge systems ⋮ \(H^{1/2}\) maps with values into the circle: minimal connections, lifting, and the Ginzburg-Landau equation ⋮ Vortex-filaments for inhomogeneous superconductors in three dimensions ⋮ Unnamed Item ⋮ On an open problem for Jacobians raised by Bourgain, Brezis and mironescu. ⋮ Line defects in the small elastic constant limit of a three-dimensional Landau-de Gennes model ⋮ Limiting Bourgain-Brezis estimates for systems of linear differential equations: theme and variations ⋮ Asymptotic behavior of critical points for a Gross-Pitaevskii energy ⋮ Rotating two-component Bose-Einstein condensates ⋮ Local $\mathbf {L}^{1}$ estimates for elliptic systems of complex vector fields ⋮ Function spaces between BMO and critical Sobolev spaces ⋮ Convergence of Ginzburg-Landau functionals in three-dimensional superconductivity ⋮ New estimates for elliptic equations and Hodge type systems ⋮ The spinor Ginzburg-Landau model in dimension three ⋮ Existence and limiting behavior of min-max solutions of the Ginzburg-Landau equations on compact manifolds ⋮ L1 Sobolev estimates for (pseudo)-differential operators and applications ⋮ Collisions and phase-vortex interactions in dissipative Ginzburg-Landau dynamics ⋮ \(p\)-adic \(L\)-functions and unitary completions of representations of \(p\)-adic reductive groups

Cites Work

• Unnamed Item
• The approximation problem for Sobolev maps between two manifolds
• On an open problem for Jacobians raised by Bourgain, Brezis and mironescu.
• The Jacobian and the Ginzburg-Landau energy
• Limiting embedding theorems for \(W^{s,p}\) when \(s\uparrow 1\) and applications
• Limiting behavior of the Ginzburg-Landau functional
• Lower bounds for the energy of \(S^ 1\)-valued maps in perforated domains
• A rigorous derivation of a free-boundary problem arising in superconductivity
• Lines vortices in the U(1) - Higgs model
• Lower Bounds for Generalized Ginzburg--Landau Functionals
• On the structure of the Sobolev space H1/2 with values into the circle

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