© 2009

Sobolev Spaces In Mathematics I

Sobolev Type Inequalities

  • Vladimir Maz’ya

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

Table of contents

  1. Front Matter
    Pages i-xxix
  2. David R. Adams
    Pages 1-23
  3. Daniel Aalto, Juha Kinnunen
    Pages 25-67
  4. Sergey Bobkov, Friedrich Götze
    Pages 69-86
  5. Donatella Danielli, Nicola Garofalo, Nguyen Cong Phuc
    Pages 117-151
  6. David E. Edmunds, W. Desmond Evans
    Pages 153-183
  7. Yehuda Pinchover, Kyril Tintarev
    Pages 281-297
  8. Back Matter
    Pages 377-378

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).


Sobolev inequlaity Sobolev inequality Sobolev space embedding functional analysis partial differential equation sharp constant

Editors and affiliations

  • Vladimir Maz’ya
    • 1
    • 2
    • 3
  1. 1.Department of MathematicsOhio State UniversityColumbusUSA
  2. 2.Department of Mathematical SciencesUniversity of LiverpoolLiverpoolUK
  3. 3.Department of MathematicsLinköping UniversityLinköpingSweden

Bibliographic information