Springer Monographs in Mathematics

Self-dual Partial Differential Systems and Their Variational Principles

Authors: Ghoussoub, Nassif

  • Contains plenty of examples and exercises
  • Includes new results which have not been previously presented in book form
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  • ISBN 978-0-387-84897-6
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About this Textbook

Based on recent research by the author and his graduate students, this text describes novel variational formulations and resolutions of a large class of partial differential equations and evolutions, many of which are not amenable to the methods of the classical calculus of variations. While it contains many new results, the general and unifying framework of the approach, its versatility in solving a disparate set of equations, and its reliance on basic functional analytic principles, makes it suitable for an intermediate level graduate course. The applications, however, require a fair knowledge of classical analysis and PDEs which is needed to make judicious choices of function spaces where the self-dual variational principles need to be applied. It is the author's hope that this material will become standard for all graduate students interested in convexity methods for PDEs.

 

Nassif Ghoussoub is a Distinguished University Professor at the University of British Columbia. He was editor-in-chief of the Canadian Journal of Mathematics for the period 1993-2003, and has served on the editorial board of various international journals. He is the founding director of the Pacific Institute for the Mathematical Sciences (PIMS), and a co-founder of the MITACS Network of Centres of Excellence. He is also the founder and scientific director of the Banff International Research Station (BIRS). He is the recipient of many awards, including the Coxeter-James, and the Jeffrey-Williams prizes. He was elected Fellow of the Royal Society of Canada in 1993, and was the recipient of a Doctorat Honoris Causa from the Universite Paris-Dauphine in 2004.

Reviews

“The subject of this monograph is related to the relationship between large classes of partial differential equations or evolutionary systems and energy functionals associated with them. Examples include transport equations, porous media equations, and Navier-Stokes evolution equations. … This well-written book contains a large amount of material. It can be useful for graduate students and researchers interested in modern aspects of the calculus of variations with powerful applications to the qualitative analysis of partial differential equations.” (Vicenţiu D. Rădulescu, zbMATH 1357.49004, 2017)

“The subject of this monograph is related to the relationship between large classes of partial differential equations or evolutionary systems and energy functionals associated with them. … This well-written book contains a large amount of material. It can be useful for graduate students and researchers interested in modern aspects of the calculus of variations with powerful applications to the qualitative analysis of partial differential equations.” (Vicentiu Rădulescu, Mathematical Reviews, Issue 2010 c)

Table of contents (18 chapters)

  • Introduction

    Ghoussoub, Nassif

    Pages 1-22

  • Legendre-Fenchel Duality on Phase Space

    Ghoussoub, Nassif

    Pages 25-48

  • Self-dual Lagrangians on Phase Space

    Ghoussoub, Nassif

    Pages 49-65

  • Skew-Adjoint Operators and Self-dual Lagrangians

    Ghoussoub, Nassif

    Pages 67-81

  • Self-dual Vector Fields and Their Calculus

    Ghoussoub, Nassif

    Pages 83-96

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-0-387-84897-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $69.95
price for USA
  • ISBN 978-0-387-84896-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $69.95
price for USA
  • ISBN 978-1-4419-2744-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Self-dual Partial Differential Systems and Their Variational Principles
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2009
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-0-387-84897-6
DOI
10.1007/978-0-387-84897-6
Hardcover ISBN
978-0-387-84896-9
Softcover ISBN
978-1-4419-2744-6
Series ISSN
1439-7382
Edition Number
1
Number of Pages
XIV, 354
Topics