Linear and Nonlinear Aspects of Vortices The Ginzburg-Landau Model

Equations of the Ginzburga?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 H?lder 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.Pacard, Frank is the author of 'Linear and Nonlinear Aspects of Vortices The Ginzburg-Landau Model' with ISBN 9780817641337 and ISBN 0817641335.