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Sobolev Spaces in Mathematics II

Applications in Analysis and Partial Differential Equations

  • 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 9)

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-xxx
    Download chapter PDF

  2. On the Mathematical Works of S.L. Sobolev in the 1930s

    • Vasilii Babich
    Pages 1-9

  3. Sobolev in Siberia

    • Yuri Reshetnyak
    Pages 11-17

  4. Boundary Harnack Principle and the Quasihyperbolic Boundary Condition

    • Hiroaki Aikawa
    Pages 19-30

  5. Sobolev Spaces and their Relatives: Local Polynomial Approximation Approach

    • Yuri Brudnyi
    Pages 31-68

  6. Spectral Stability of Higher Order Uniformly Elliptic Operators

    • Victor Burenkov, Pier Domenico Lamberti
    Pages 69-102

  7. Conductor Inequalities and Criteria for Sobolev-Lorentz Two-Weight Inequalities

    • Serban Costea, Vladimir Maz'ya
    Pages 103-121

  8. Besov Regularity for the Poisson Equation in Smooth and Polyhedral Cones

    • Stephan Dahlke, Winfried Sickel
    Pages 123-145

  9. Variational Approach to Complicated Similarity Solutions of Higher Order Nonlinear Evolution Partial Differential Equations

    • Victor Galaktionov, Enzo Mitidieri, Stanislav Pokhozhaev
    Pages 147-197

  10. L q,p -Cohomology of Riemannian Manifolds with Negative Curvature

    • Vladimir Gol'dshtein, Marc Troyanov
    Pages 199-208

  11. Volume Growth and Escape Rate of Brownian Motion on a Cartan—Hadamard Manifold

    • Alexander Grigor'yan, Elton Hsu
    Pages 209-225

  12. Sobolev Estimates for the Green Potential Associated with the Robin—Laplacian in Lipschitz Domains Satisfying a Uniform Exterior Ball Condition

    • Tünde Jakab, Irina Mitrea, Marius Mitrea
    Pages 227-260

  13. Properties of Spectra of Boundary Value Problems in Cylindrical and Quasicylindrical Domains

    • Sergey Nazarov
    Pages 261-309

  14. Estimates for Completely Integrable Systems of Differential Operators and Applications

    • Yuri Reshetnyak
    Pages 311-327

  15. Counting Schrödinger Boundstates: Semiclassics and Beyond

    • Grigori Rozenblum, Michael Solomyak
    Pages 329-353

  16. Function Spaces on Cellular Domains

    • Hans Triebel
    Pages 355-385

  17. Back Matter

    Pages 387-388
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Keywords

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 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 integration 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 1930s and the foundation of Akademgorodok in Siberia, supplied with unique archive photos of S. Sobolev are included.

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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