Two results on entire solutions of Ginzburg-Landau system in higher dimensions

DOI10.1016/j.jfa.2003.07.012zbMath1183.35127OpenAlexW2056133328MaRDI QIDQ1882964

Alberto Farina

Publication date: 1 October 2004

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2003.07.012

zbMATH Keywords

SymmetryLiouville-type theoremsGinzburg-Landau systemsNonlinear elliptic systems of PDE

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Nonlinear elliptic equations (35J60)

Related Items (13)

Gradient map of isoparametric polynomial and its application to Ginzburg-Landau system ⋮ Some remarks on energy inequalities for harmonic maps with potential ⋮ New explicit solutions to the \(p\)-Laplace equation based on isoparametric foliations ⋮ Two results on the equivariant Ginzburg-Landau vortex in arbitrary dimension ⋮ A Liouville type result and quantization effects on the system \(-\Delta u = u J'(1-|u|^2)\) for a potential convex near zero ⋮ Symmetry and asymmetry of components for elliptic Gross-Pitaevskii system ⋮ One-dimensional symmetry and Liouville type results for the fourth order Allen-Cahn equation in \(\mathbb{R}^N\) ⋮ Symmetry in nonlinear PDEs: some open problems ⋮ On the growth of the energy of entire solutions to the vector Allen-Cahn equation ⋮ A LIOUVILLE PROPERTY FOR GINZBURG–LANDAU SYSTEMS ⋮ Spectral properties of nonassociative algebras and breaking regularity for nonlinear elliptic type PDEs ⋮ Some basic facts on the system $\Delta u - W_{u} (u) = 0$ ⋮ Density estimates for vector minimizers and applications

Cites Work

• Examples of harmonic maps from disks to hemispheres
• Some properties of solutions of the Ginzburg-Landau equation on an open set of \(\mathbb{R}^ 2\)
• Quantization effects for \(-\Delta u=u(1-| u|^ 2)\) in \(\mathbb{R}^ 2\)
• Qualitative study of radial solutions of the Ginzburg-Landau system in \(\mathbb{R}^N\) \((N\geq 3)\)
• Finite energy solutions, quantization effects and Liouville-type results for a variant of the Ginzburg-Landau systems in \(\mathbb R^K\).
• A qualitative study of the real solutions of an ordinary differential equation related to the Ginzburg-Landau equation
• Polynomial maps from spheres to spheres
• Lines vortices in the U(1) - Higgs model
• Harmonic Maps and Minimal Immersions with Symmetries (AM-130)
• A gradient bound and a liouville theorem for nonlinear poisson equations
• Shooting method for vortex solutions of a complex-valued Ginzburg–Landau equation
• Sur les solutions radiales de l'équation −Δu = u(1 − ¦u¦2) dans ℝN (N ≥ 3)
• Spiral Waves in Reaction-Diffusion Equations
• Ginzburg-Landau vortices
• Asymptotics for the Ginzburg-Landau equation in arbitrary dimensions
• Unnamed Item
• Unnamed Item

This page was built for publication: Two results on entire solutions of Ginzburg-Landau system in higher dimensions