Sobolev Spaces in Mathematics II

Applications in Analysis and Partial Differential Equations

  • Vladimir Maz'ya

Part of the International Mathematical Series book series (IMAT, volume 9)

Table of contents

  1. Front Matter
    Pages i-xxx
  2. Yuri Reshetnyak
    Pages 11-17
  3. Victor Burenkov, Pier Domenico Lamberti
    Pages 69-102
  4. Stephan Dahlke, Winfried Sickel
    Pages 123-145
  5. Vladimir Gol'dshtein, Marc Troyanov
    Pages 199-208
  6. Grigori Rozenblum, Michael Solomyak
    Pages 329-353
  7. Hans Triebel
    Pages 355-385
  8. Back Matter
    Pages 387-388

About this book


Sobolev spaces become the established and universal language of partial differential equations and mathematical analysis. Among a huge variety of problems where Sobolev spaces are used, the following important topics are in the focus of this volume: boundary value problems in domains with singularities, higher order partial differential equations, local polynomial approximations, inequalities in Sobolev-Lorentz spaces, function spaces in cellular domains, the spectrum of a Schrodinger operator with negative potential and other spectral problems, criteria for the complete integrability of systems of differential equations with applications to differential geometry, some aspects of differential forms on Riemannian manifolds related to Sobolev inequalities, Brownian motion on a Cartan-Hadamard manifold, etc. Two short biographical articles on the works of Sobolev in the 1930's and foundation of Akademgorodok in Siberia, supplied with unique archive photos of S. Sobolev are included.

Contributors include: Vasilii Babich (Russia); Yuri Reshetnyak (Russia); Hiroaki Aikawa (Japan); Yuri Brudnyi (Israel); Victor Burenkov (Italy) and Pier Domenico Lamberti (Italy); Serban Costea (Canada) and Vladimir Maz'ya (USA-UK-Sweden); Stephan Dahlke (Germany) and Winfried Sickel (Germany); Victor Galaktionov (UK), Enzo Mitidieri (Italy), and Stanislav Pokhozhaev (Russia); Vladimir Gol'dshtein (Israel) and Marc Troyanov (Switzerland); Alexander Grigor'yan (Germany) and Elton Hsu (USA); Tunde Jakab (USA), Irina Mitrea (USA), and Marius Mitrea (USA); Sergey Nazarov (Russia); Grigori Rozenblum (Sweden) and Michael Solomyak (Israel); Hans Triebel (Germany)


Boundary value problem Potential Sobolev space analysis mathematical physics partial differential equation spectral problem

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