Locally minimising solutions of − Δu = u(1 − |u|2) in R2

DOI10.1017/S030821050001283XzbMath0905.35018OpenAlexW2330890417MaRDI QIDQ3840010

Etienne Sandier

Publication date: 10 August 1998

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s030821050001283x

zbMATH Keywords

Ginzburg-Landau functionalenergy estimatecomparison function

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) A priori estimates in context of PDEs (35B45) Variational methods for second-order elliptic equations (35J20)

Related Items (8)

Interacting helical traveling waves for the Gross-Pitaevskii equation ⋮ On the limit \(p\to\infty\) of global minimizers for a \(p\)-Ginzburg-Landau-type energy ⋮ Small energy Ginzburg-Landau minimizers in \(\mathbb{R}^3\) ⋮ Vortex collisions and energy-dissipation rates in the Ginzburg-Landau heat flow. I: Study of the perturbed Ginzburg-Landau equation ⋮ Global minimizers for a \(p\)-Ginzburg-Landau-type energy in \(\mathbb R^2\) ⋮ Asymptotic estimates for an integral equation in theory of phase transition ⋮ Interacting helical vortex filaments in the three-dimensional Ginzburg-Landau equation ⋮ Vortex helices for the Gross-Pitaevskii equation

Cites Work

• Some properties of solutions of the Ginzburg-Landau equation on an open set of \(\mathbb{R}^ 2\)
• Asymptotics for the minimization of a Ginzburg-Landau functional
• Quantization effects for \(-\Delta u=u(1-| u|^ 2)\) in \(\mathbb{R}^ 2\)
• Vortices for a variational problem related to superconductivity

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