Solutions with vortices of a semi-stiff boundary value problem for the Ginzburg-Landau equation

DOI10.4171/JEMS/239zbMath1205.35300arXiv0712.1062OpenAlexW2054934031MaRDI QIDQ604442

Volodymyr Rybalko, Leonid Berlyand

Publication date: 11 November 2010

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0712.1062

zbMATH Keywords

Ginzburg-Landau equationNeumann conditionDirichlet conditionGinzburg-Landau energy functionalstable solution

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Variational methods for second-order elliptic equations (35J20) Variational methods applied to problems in optics and electromagnetic theory (78M30) Ginzburg-Landau equations (35Q56)

Related Items (8)

Near boundary vortices in a magnetic Ginzburg-Landau model: their locations via tight energy bounds ⋮ Local minimizers of the Ginzburg-Landau functional with prescribed degrees ⋮ Harmonic maps with prescribed degrees on the boundary of an annulus and bifurcation of catenoids ⋮ Renormalized energies for unit-valued harmonic maps in multiply connected domains ⋮ Existence of critical points with semi-stiff boundary conditions for singular perturbation problems in simply connected planar domains ⋮ Size of planar domains and existence of minimizers of the Ginzburg-Landau energy with semistiff boundary conditions ⋮ Insertion of bubbles at the boundary for the Ginzburg-Landau functional ⋮ Minimax Critical Points in Ginzburg-Landau Problems with Semi-Stiff Boundary Conditions: Existence and Bubbling

Cites Work

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• Ginzburg-Landau minimizers with prescribed degrees. capacity of the domain and emergence of vortices
• Topological methods for the Ginzburg-Landau equations
• Vortex pinning with bounded fields for the Ginzburg-Landau equation.
• Ginzburg--Landau minimizers with prescribed degrees: Dependence on domain.
• Topological sectors for Ginzburg-Landau energies
• Nonexistence of Ginzburg-Landau minimizers with prescribed degree on the boundary of a doubly connected domain
• Vortices and pinning effects for the Ginzburg-Landau model in multiply connected domains

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