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 Holder 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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