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

Book 9 of 53: Progress in Nonlinear Differential Equations and Their Applications

Pacard, Frank; Riviere, Tristan

 
9780817641337: Linear and Nonlinear Aspects of Vortices: The Ginzburg-andau Model: 39 (Progress in Nonlinear Differential Equations and Their Applications, 39)

Synopsis

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.

"synopsis" may belong to another edition of this title.

Review

"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

Synopsis

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 non-linear 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 graduate students, this monographs should be useful in a number of contexts in the non-linear analysis of problems arising in geometry or mathematical physics. The material presented covers recent and original results by the authors, and should serve as an classroom text or a self-study resource.

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