Local minimizers of the Ginzburg-Landau energy with magnetic field in three dimensions

DOI10.1007/s00220-004-1082-yzbMath1065.58012OpenAlexW1985533088MaRDI QIDQ1771546

Alberto Montero, Peter Sternberg, Robert Leon Jerrard

Publication date: 18 April 2005

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00220-004-1082-y

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Singular perturbations in context of PDEs (35B25) Nonlinear elliptic equations (35J60) Variational methods for elliptic systems (35J50) Methods involving semicontinuity and convergence; relaxation (49J45) Statistical mechanics of superconductors (82D55) Applications of variational problems in infinite-dimensional spaces to the sciences (58E50)

Related Items (18)

Variational modeling of dislocations in crystals in the line-tension limit ⋮ Critical points via \(\Gamma \)-convergence: general theory and applications ⋮ Bounded vorticity for the 3D Ginzburg–Landau model and an isoflux problem ⋮ Vortices in the three-dimensional thin-film Ginzburg-Landau model of superconductivity ⋮ Calculus of variations. Abstracts from the workshop held August 14--20, 2022 ⋮ Vortex density models for superconductivity and superfluidity ⋮ Hodge decomposition with degenerate weights and the Gross-Pitaevskii energy ⋮ Entire solutions to 4 dimensional Ginzburg-Landau equations and codimension 2 minimal submanifolds ⋮ Three dimensional vortex approximation construction and \({\epsilon}\)-level estimates for the Ginzburg-Landau functional ⋮ Local minimizers with vortex pinning to Ginzburg-Landau functional in three dimensions ⋮ On the first critical field in the three dimensional Ginzburg-Landau model of superconductivity ⋮ Vortices for a rotating toroidal Bose-Einstein condensate ⋮ On the Ginzburg-Landau model of a superconducting ball in a uniform field ⋮ Pinning of magnetic vortices by an external potential ⋮ \(\Gamma\)-convergence and the emergence of vortices for Ginzburg-Landau on thin shells and manifolds ⋮ On the first critical field in Ginzburg-Landau theory for thin shells and manifolds ⋮ Convergence of Ginzburg-Landau functionals in three-dimensional superconductivity ⋮ Local minimizers with vortex filaments for a Gross-Pitaevsky functional

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Ginzburg-Landau equation with magnetic effect: non-simply-connected domains
• An introduction to \(\Gamma\)-convergence
• Domain variation for certain sets of solutions and applications
• Functions with prescribed singularities
• Magnetic bottles for the Neumann problem: the case of dimension 3
• The Jacobian and the Ginzburg-Landau energy
• Domain perturbation method and local minimizers to Ginzburg-Landau functional with magnetic effect
• Surface nucleation of superconductivity in 3-dimensions
• Limiting behavior of the Ginzburg-Landau functional
• Vortices for a variational problem related to superconductivity
• Homotopy classification of minimizers of the Ginzburg-Landau energy and the existence of permanent currents
• Complex Ginzburg-Landau equations in high dimensions and codimension two area minimizing currents
• Lines vortices in the U(1) - Higgs model
• Local minimisers and singular perturbations
• The Breakdown of Superconductivity Due to Strong Fields for the Ginzburg--Landau Model
• Stability of nonconstant steady-state solutions to a Ginzburg–Landau equation in higher space dimensions
• Functions of bounded higher variation
• Local minimizers with vortices to the Ginzburg-Landau system in three dimensions
• LOCAL MINIMIZERS FOR THE GINZBURG–LANDAU ENERGY NEAR CRITICAL MAGNETIC FIELD: PART II
• ON THE ENERGY OF TYPE-II SUPERCONDUCTORS IN THE MIXED PHASE
• Small energy solutions to the Ginzburg–Landau equation
• Ginzburg-Landau minimizers from R^{n+1} to R^n and minimal connections
• Stability in 2D Ginzburg-Landau passes to the limit
• Nonexistence of Permanent Currents in Convex Planar Samples
• Ginzburg–Landau Equations and Stable Solutions in a Rotational Domain
• Variational convergence for functionals of Ginzburg-Landau type
• Asymptotics for the Ginzburg-Landau equation in arbitrary dimensions

This page was built for publication: Local minimizers of the Ginzburg-Landau energy with magnetic field in three dimensions