Universitext

Functional Analysis, Sobolev Spaces and Partial Differential Equations

Authors: Brezis, Haim

  • Major textbook by a well-known and highly regarded author
  • The first single-volume textbook to cover related fields of functional analysis and PDEs
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eBook $64.99
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  • ISBN 978-0-387-70914-7
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  • Immediate eBook download after purchase
Softcover $84.95
price for USA
  • ISBN 978-0-387-70913-0
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  • Usually dispatched within 3 to 5 business days.
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About this Textbook

Uniquely, this book presents a coherent, concise and unified way of combining elements from two distinct “worlds,” functional analysis (FA) and partial differential equations (PDEs), and is intended for students who have a good background in real analysis. This text presents a smooth transition from FA to PDEs by analyzing in great detail the simple case of one-dimensional PDEs (i.e., ODEs), a more manageable approach for the beginner. Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Moreover, the wealth of exercises and additional material presented, leads the reader to the frontier of research. This book has its roots in a celebrated course taught by the author for many years and is a completely revised, updated, and expanded English edition of the important “Analyse Fonctionnelle” (1983). Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English version is a welcome addition to this list. The first part of the text deals with abstract results in FA and operator theory. The second part is concerned with the study of spaces of functions (of one or more real variables) having specific differentiability properties, e.g., the celebrated Sobolev spaces, which lie at the heart of the modern theory of PDEs. The Sobolev spaces occur in a wide range of questions, both in pure and applied mathematics, appearing in linear and nonlinear PDEs which arise, for example, in differential geometry, harmonic analysis, engineering, mechanics, physics etc. and belong in the toolbox of any graduate student studying analysis.

Reviews

From the reviews:

“Brezis has intelligently chosen several fundamental concepts of functional analysis, and has build the book around them and their applications. … for a newcomer who intends to become a user of functional analysis this book is an ideal place to start. In fact I would recommend this over any other source to any beginning graduate student. … the book also has all the basic tools for a beginer PDE researcher … . Its a bible for the field of research.” (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, October, 2013)

“This textbook has its origin in the French version Analyse fonctionnelle published in 1985, which has become a standard reference and was translated into several languages. … At the end of each chapter the reader will find comments with further information, references, and historic remarks. … In summary, the present textbook provides an excellent basis for a course on functional analysis plus a follow-up course on partial differential equations. It is well-written and I can wholeheartedly recommend it to both students and teachers.” (G. Teschl, Monatshefte für Mathematik, Vol. 165 (3-4), March, 2012)

“This book is a tour de force by the author, who is a master of modern nonlinear functional analysis and who has contributed extensively to the development of the theory of partial differential equations. … The writing is lively, the material is diverse and maintains a strong unity. … the book is a very useful contribution to the growing literature on this circle of ideas. I wholeheartedly recommend this book both as a textbook, as well as for independent study.” (Vicenţiu Rădulescu, Mathematical Reviews, Issue 2012 a)

“The book is the English translation of an 1983 book published in French: Analyse fonctionnelle :théorie et applications … . It has seen translations into numerous languages and the Springer edition was especially anticipated, as it announced a number of practice exercises following each chapter. I can honestly say that it was well worth the wait. … The text is a pleasure to read. … I wholeheartedly recommend this book as both a textbook as well as for independent study.” (Florin Catrina, The Mathematical Association of America, June, 2011)


Table of contents (11 chapters)

  • The Hahn–Banach Theorems. Introduction to the Theory of Conjugate Convex Functions

    Brezis, Haim

    Pages 1-29

  • The Uniform Boundedness Principle and the Closed Graph Theorem

    Brezis, Haim

    Pages 31-54

  • Weak Topologies. Reflexive Spaces. Separable Spaces. Uniform Convexity

    Brezis, Haim

    Pages 55-87

  • Lp Spaces

    Brezis, Haim

    Pages 89-130

  • Hilbert Spaces

    Brezis, Haim

    Pages 131-156

Buy this book

eBook $64.99
price for USA (gross)
  • ISBN 978-0-387-70914-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $84.95
price for USA
  • ISBN 978-0-387-70913-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Functional Analysis, Sobolev Spaces and Partial Differential Equations
Authors
Series Title
Universitext
Copyright
2011
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-0-387-70914-7
DOI
10.1007/978-0-387-70914-7
Softcover ISBN
978-0-387-70913-0
Series ISSN
0172-5939
Edition Number
1
Number of Pages
XIV, 600
Number of Illustrations and Tables
9 b/w illustrations
Topics