Linear and Nonlinear Aspects of Vortices: The Ginzburg-andau Model: 39 (Progress in Nonlinear Differential Equations and Their Applications) - Softcover

Pacard, Frank; Riviere, Tristan

Softcover

ISBN 10: 1461271258 ISBN 13: 9781461271253

Verlag: Birkhäuser, 2012

Inhaltsangabe

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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Críticas

"In the course of their argument, the authors traverse a broad range of nontrivial analysis: elliptic equations on weighted Holder and Sobolev spaces, radially symmetric solutions, gluing techniques, Pokhozhaev-type arguments for solutions of semilinear elliptic equations, and more. Clearly aimed at a research audience, this book provides a fascinating and original account of the theory of Ginzburg-Landau vortices."

--Mathematical Reviews

Reseña del editor

Aimed at mathematicians, physicists, engineers, and grad students, this monograph will be useful for the nonlinear analysis of problems arising in geometry or mathematical physics. The material presented covers recent and original results by the authors, and serves as an excellent classroom text or a valuable self-study resource.

Details zur Ausgabe

• Verlag: Birkhäuser
• Erscheinungsdatum: 2012
• ISBN 10: 1461271258
• ISBN 13: 9781461271253
• Einband: Tapa blanda
• Sprache: Englisch
• Anzahl der Seiten: 356
• Kontakt zum Hersteller: Nicht verfügbar