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Sobolev Spaces in Mathematics I

Sobolev Type Inequalities

  • Book
  • © 2009

Overview

Editors:
  1. Vladimir Maz’ya

    1. Department of Mathematics, Ohio State University, Columbus, USA
      Department of Mathematical Sciences, University of Liverpool, Liverpool, UK
      Department of Mathematics, Linköping University, Linköping, Sweden

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  • Presentation of new results on the latest topics of the theory Sobolev spaces, partial differential equations, analysis and mathematical physics
  • The authors and editors are world-known 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 been published earlier in the English-language literature
  • Includes supplementary material: sn.pub/extras

Part of the book series: International Mathematical Series (IMAT, volume 8)

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xxix
    Download chapter PDF

  2. My Love Affair with the Sobolev Inequality

    • David R. Adams
    Pages 1-23

  3. Maximal Functions in Sobolev Spaces

    • Daniel Aalto, Juha Kinnunen
    Pages 25-67

  4. Hardy Type Inequalities via Riccati and Sturm–Liouville Equations

    • Sergey Bobkov, Friedrich Götze
    Pages 69-86

  5. Quantitative Sobolev and Hardy Inequalities, and Related Symmetrization Principles

    • Andrea Cianchi
    Pages 87-116

  6. Inequalities of Hardy–Sobolev Type in Carnot–Carathéodory Spaces

    • Donatella Danielli, Nicola Garofalo, Nguyen Cong Phuc
    Pages 117-151

  7. Sobolev Embeddings and Hardy Operators

    • David E. Edmunds, W. Desmond Evans
    Pages 153-183

  8. Sobolev Mappings between Manifolds and Metric Spaces

    • Piotr Hajlasz
    Pages 185-222

  9. A Collection of Sharp Dilation Invariant Integral Inequalities for Differentiable Functions

    • Vladimir Maz'ya, Tatyana Shaposhnikova
    Pages 223-247

  10. Optimality of Function Spaces in Sobolev Embeddings

    • Luboš Pick
    Pages 249-280

  11. On the Hardy–Sobolev–Maz'ya Inequality and Its Generalizations

    • Yehuda Pinchover, Kyril Tintarev
    Pages 281-297

  12. Sobolev Inequalities in Familiar and Unfamiliar Settings

    • Laurent Saloff-Coste
    Pages 299-343

  13. A Universality Property of Sobolev Spaces in Metric Measure Spaces

    • Nageswari Shanmugalingam
    Pages 345-359

  14. Cocompact Imbeddings and Structure of Weakly Convergent Sequences

    • Kiril Tintarev
    Pages 361-376

  15. Back Matter

    Pages 377-378
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Keywords

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).

Editors and Affiliations

  • Department of Mathematics, Ohio State University, Columbus, USA

    Vladimir Maz’ya

  • Department of Mathematical Sciences, University of Liverpool, Liverpool, UK

    Vladimir Maz’ya

  • Department of Mathematics, Linköping University, Linköping, Sweden

    Vladimir Maz’ya

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