Ginzburg-Landau Vortices / Edition 1

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Editorial Reviews

From the Publisher
"The three authors are well-known excellent specialists in nonlinear functional analysis and partial differential equations and the material presented in the book covers some of their recent and original results. The book is written in a very clear and readable style with many examples."


"...the book gives a very stimulating account of an interesting minimization problem. It can be a fruitful source of ideas for those who work through the material carefully."


A textbook for a one-semester graduate course, assuming knowledge of nonlinear functional analysis, partial differential equations, and complex functions. Deals with problems that arise in studying phase transitions in superconductors and superfluids. Annotation c. Book News, Inc., Portland, OR (
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Product Details

Table of Contents

I Energy estimates for S[superscript 1]-valued maps
II A lower bound for the energy of S[superscript 1]-valued maps on perforated domains
III Some basic estimates for u[subscript [epsilon]]
IV Towards locating the singularities: bad discs and good discs
V An upper bound for the energy of u[subscript [epsilon]] away from the singularities
VI [actual symbol not reproducible] converges: u[subscript *] is born!
VII u[subscript *] coincides with THE canonical harmonic map having singularities (a[subscript j])
VIII The configuration (a[subscript j]) minimizes the renormalized energy W
IX Some additional properties of u[subscript [epsilon]]
X Non minimizing solutions of the Ginzburg-Landau equation
XI Open problems
Appendix I. Summary of the basic convergence results in the case where deg(g,[actual symbol not reproducible]G) = 0
Appendix II. Radial solutions
Appendix III. Quantization effects for the equation [actual symbol not reproducible]
Appendix W. The energy of maps on perforated domains revisited
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