EAN: 9781461271253

LINEAR AND NONLINEAR ASPECTS OF VORTICES - FRAN...

Equations of the Ginzburg-Landau vortices have particular applications to a number of problems
in physics  including phase transition phenomena in superconductors  superfluids  and liquid
crystals. Building on the results presented by Bethuel  Brazis  and Helein  this current work
further analyzes Ginzburg-Landau vortices with a particular emphasis on the uniqueness
question. The authors begin with a general presentation of the theory and then proceed to study
problems using weighted Hölder spaces and Sobolev Spaces. These are particularly powerful tools
and help us obtain a deeper understanding of the nonlinear partial differential equations
associated with Ginzburg-Landau vortices. Such an approach sheds new light on the links between
the geometry of vortices and the number of solutions. Aimed at mathematicians  physicists 
engineers  and grad students  this monograph will be useful in a number of contexts in the
nonlinear analysis of problems arising in geometry or mathematical physics. The material
presented covers recent and original results by the authors  and will serve as an excellent
classroom text or a valuable self-study resource.

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