Ginzburg-Landau Vortices
Authors: Bethuel, Fabrice, Brezis, Haim, Helein, Frederic
Free Preview- Affordable, softcover reprint of a classic textbook
- Authors are well-known specialists in nonlinear functional analysis and partial differential equations
- Written in a clear, readable style with many examples
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- About this book
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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 parameter ɛ has a dimension of a length which is usually small. Thus, it is of great interest to study the asymptotics as ɛ tends to zero.
One of the main results asserts that the limit u-star of minimizers uɛ exists. Moreover, u-star is smooth except at a finite number of points called defects or vortices in physics. The number of these defects is exactly the Brouwer degree – or winding number – of the boundary condition. Each singularity has degree one – or as physicists would say, vortices are quantized.
The material presented in this book covers mostly original results by the authors. It assumes a moderate knowledge of nonlinear functional analysis, partial differential equations, and complex functions. This book is designed for researchers and graduate students alike, and can be used as a one-semester text. The present softcover reprint is designed to make this classic text available to a wider audience.
- Table of contents (11 chapters)
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Energy estimates for S-valued maps
Pages 1-30
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The lower bound for the energy of S-valued maps on Perforated domains
Pages 31-41
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Some basic estimateds for UE
Pages 42-47
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Towards locating the singularties: bad discs and good discs
Pages 48-51
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An upper bound for the energy of UE away for the singularities
Pages 52-56
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Table of contents (11 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Ginzburg-Landau Vortices
- Authors
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- Fabrice Bethuel
- Haim Brezis
- Frederic Helein
- Series Title
- Modern Birkhäuser Classics
- Copyright
- 2017
- Publisher
- Birkhäuser Basel
- Copyright Holder
- Springer International Publishing AG
- eBook ISBN
- 978-3-319-66673-0
- DOI
- 10.1007/978-3-319-66673-0
- Softcover ISBN
- 978-3-319-66672-3
- Series ISSN
- 2197-1803
- Edition Number
- 1
- Number of Pages
- XXIX, 159
- Number of Illustrations
- 4 b/w illustrations, 1 illustrations in colour
- Topics
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