International Mathematical Series

Sobolev Spaces in Mathematics I

Sobolev Type Inequalities

Editors: Maz'ya, Vladimir (Ed.)

  • Presentation of new results on the latest topics of the theory of Sobolev spaces, partial differential equations, analysis and mathematical physics
  • The authors and editors are world-renowned specialists, working in different countries
  • Publication on the centenary of Sobolev’s birth with two short biographical articles and unique archive photos of S. Sobolev which have not yet been published in the English-language literature
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Hardcover $259.00
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Softcover $259.00
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About this book

This volume is dedicated to the centenary of the outstanding mathematician of the XXth century Sergey Sobolev and, in a sense, to his celebrated work On a theorem of functional analysis published in 1938, exactly 70 years ago, where the original Sobolev inequality was proved. This double event is a good case to gather experts for presenting the latest results on the study of Sobolev inequalities which play a fundamental role in analysis, the theory of partial differential equations, mathematical physics, and differential geometry. In particular, the following topics are discussed: Sobolev type inequalities on manifolds and metric measure spaces, traces, inequalities with weights, unfamiliar settings of Sobolev type inequalities, Sobolev mappings between manifolds and vector spaces, properties of maximal functions in Sobolev spaces, the sharpness of constants in inequalities, etc. The volume opens with a nice survey reminiscence My Love Affair with the Sobolev Inequality by David R. Adams.

Contributors include: David R. Adams (USA); Daniel Aalto (Finland) and Juha Kinnunen (Finland); Sergey Bobkov (USA) and Friedrich Götze (Germany); Andrea Cianchi (Italy); Donatella Danielli (USA), Nicola Garofalo (USA), and Nguyen Cong Phuc (USA); David E. Edmunds (UK) and W. Desmond Evans (UK); Piotr Hajlasz (USA); Vladimir Maz'ya (USA-UK-Sweden) and Tatyana Shaposhnikova USA-Sweden); Luboš Pick (Czech Republic); Yehuda Pinchover (Israel) and Kyril Tintarev (Sweden); Laurent Saloff-Coste (USA); Nageswari Shanmugalingam (USA).

Table of contents (13 chapters)

  • My Love Affair with the Sobolev Inequality

    Adams, David R.

    Pages 1-23

  • Maximal Functions in Sobolev Spaces

    Aalto, Daniel (et al.)

    Pages 25-67

  • Hardy Type Inequalities via Riccati and Sturm–Liouville Equations

    Bobkov, Sergey (et al.)

    Pages 69-86

  • Quantitative Sobolev and Hardy Inequalities, and Related Symmetrization Principles

    Cianchi, Andrea

    Pages 87-116

  • Inequalities of Hardy–Sobolev Type in Carnot–Carathéodory Spaces

    Danielli, Donatella (et al.)

    Pages 117-151

Buy this book

eBook $199.00
price for USA (gross)
  • ISBN 978-0-387-85648-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $259.00
price for USA
  • ISBN 978-0-387-85647-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $259.00
price for USA
  • ISBN 978-1-4419-2757-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Sobolev Spaces in Mathematics I
Book Subtitle
Sobolev Type Inequalities
Editors
  • Vladimir Maz'ya
Series Title
International Mathematical Series
Series Volume
8
Copyright
2009
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-0-387-85648-3
DOI
10.1007/978-0-387-85648-3
Hardcover ISBN
978-0-387-85647-6
Softcover ISBN
978-1-4419-2757-6
Series ISSN
1571-5485
Edition Number
1
Number of Pages
XXX, 378
Additional Information
Jointly published with Tamara Rozhkovskaya Publisher, Novosibirsk, Russia
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