Ginzburg-Landau Vortices

• Main Authors: Bethuel, Fabrice (Author), Brezis, Haim (Author), Helein, Frederic (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2017.
• Series: Modern Birkhäuser Classics,
• Subjects: Mathematics.; Partial differential equations.; Mathematical physics.; Partial Differential Equations.; Mathematical Applications in the Physical Sciences.

This book is concerned with the study in two dimensions of stationary solutions of uɛ of a complex valued Ginzburg-Landau equation involving a small parameter ɛ. Such problems are related to questions occurring in physics, e.g., phase transition phenomena in superconductors and superfluids. The para...

Table of Contents:

• Introduction
• Energy Estimates for S1-Valued Maps
• A Lower Bound for the Energy of S1-Valued Maps on Perforated Domains
• Some Basic Estimates for uɛ
• Toward Locating the Singularities: Bad Discs and Good Discs
• An Upper Bound for the Energy of uɛ away from the Singularities
• uɛ_n: u-star is Born! - u-star Coincides with THE Canonical Harmonic Map having Singularities (aj)
• The Configuration (aj) Minimizes the Renormalization Energy W
• Some Additional Properties of uɛ
• Non-Minimizing Solutions of the Ginzburg-Landau Equation
• Open Problems.