BOUNDARY PROBLEMS FOR THE GINZBURG–LANDAU EQUATION

DOI10.1142/S0219199705001908zbMath1124.35081MaRDI QIDQ5714693

David Chiron

Publication date: 15 December 2005

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

zbMATH Keywords

boundary problemsNeumann conditionGinzburg-Landau vortexDirichlet datumanchoring condition

Mathematics Subject Classification ID

Variational methods involving nonlinear operators (47J30) Boundary value problems for second-order elliptic equations (35J25) Singular perturbations in context of PDEs (35B25) Nonlinear elliptic equations (35J60) Geometric measure and integration theory, integral and normal currents in optimization (49Q15) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items (8)

Critical points via \(\Gamma \)-convergence: general theory and applications ⋮ Unnamed Item ⋮ On the first critical field in the three dimensional Ginzburg-Landau model of superconductivity ⋮ On the NLS dynamics for infinite energy vortex configurations on the plane ⋮ On the Ginzburg-Landau model of a superconducting ball in a uniform field ⋮ Convergence of Ginzburg-Landau functionals in three-dimensional superconductivity ⋮ Asymptotics for the Ginzburg-Landau equation on manifolds with boundary under homogeneous Neumann condition ⋮ Vortex helices for the Gross-Pitaevskii equation

Cites Work

• Semilinear equations in \({\mathbb{R}}^ N\) without condition at infinity
• From Ginzburg-Landau to Gross-Pitaevskii
• The Jacobian and the Ginzburg-Landau energy
• Complex Ginzburg-Landau equations in high dimensions and codimension two area minimizing currents
• Schrödinger operators with singular potentials
• Lines vortices in the U(1) - Higgs model
• Elliptic Partial Differential Equations of Second Order
• Uniform estimates for the parabolic Ginzburg–Landau equation
• Asymptotics for the Ginzburg-Landau equation in arbitrary dimensions

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