Linear and Nonlinear Aspects of Vortices - Frank Pacard Tristan Riviere Kartoniert (TB)

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 understandi ng 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.