Ebook: Ginzburg-Landau Vortices

"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."

--ZAA

"...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."

--ZAMP

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Content:
Front Matter....Pages i-xxvii
Energy estimates for S1-valued maps....Pages 1-30
A lower bound for the energy of S1-valued maps on perforated domains....Pages 31-41
Some basic estimates for u ? ....Pages 42-47
Towards locating the singularities: bad discs and good discs....Pages 48-51
An upper bound for the energy of u ? away from the singularities....Pages 52-56
u ?n converges: u ? is born!....Pages 57-64
u ? coincides with THE canonical harmonic map having singularities (a j )....Pages 65-75
The configuration (a j) minimizes the renormalized energy W ....Pages 76-99
Some additional properties of u? ....Pages 100-106
Non-minimizing solutions of the Ginzburg-Landau equation....Pages 107-136
Open problems....Pages 137-141
Back Matter....Pages 142-162

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Content:
Front Matter....Pages i-xxvii
Energy estimates for S1-valued maps....Pages 1-30
A lower bound for the energy of S1-valued maps on perforated domains....Pages 31-41
Some basic estimates for u ? ....Pages 42-47
Towards locating the singularities: bad discs and good discs....Pages 48-51
An upper bound for the energy of u ? away from the singularities....Pages 52-56
u ?n converges: u ? is born!....Pages 57-64
u ? coincides with THE canonical harmonic map having singularities (a j )....Pages 65-75
The configuration (a j) minimizes the renormalized energy W ....Pages 76-99
Some additional properties of u? ....Pages 100-106
Non-minimizing solutions of the Ginzburg-Landau equation....Pages 107-136
Open problems....Pages 137-141
Back Matter....Pages 142-162
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