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Lebesgue and Sobolev Spaces with Variable Exponents

  • Lars Diening
  • Petteri Harjulehto
  • Peter Hästö
  • Michael Ruzicka

Part of the Lecture Notes in Mathematics book series (LNM, volume 2017)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Lars Diening, Petteri Harjulehto, Peter Hästö, Michael Růžička
    Pages 1-17
  3. Lebesgue Spaces

    1. Front Matter
      Pages 19-19
    2. Lars Diening, Petteri Harjulehto, Peter Hästö, Michael Růžička
      Pages 21-68
    3. Lars Diening, Petteri Harjulehto, Peter Hästö, Michael Růžička
      Pages 69-97
    4. Lars Diening, Petteri Harjulehto, Peter Hästö, Michael Růžička
      Pages 99-141
    5. Lars Diening, Petteri Harjulehto, Peter Hästö, Michael Růžička
      Pages 143-197
    6. Lars Diening, Petteri Harjulehto, Peter Hästö, Michael Růžička
      Pages 199-212
    7. Lars Diening, Petteri Harjulehto, Peter Hästö, Michael Růžička
      Pages 213-244
  4. Sobolev Spaces

    1. Front Matter
      Pages 245-245
    2. Lars Diening, Petteri Harjulehto, Peter Hästö, Michael Růžička
      Pages 247-288
    3. Lars Diening, Petteri Harjulehto, Peter Hästö, Michael Růžička
      Pages 289-314
    4. Lars Diening, Petteri Harjulehto, Peter Hästö, Michael Růžička
      Pages 315-338
    5. Lars Diening, Petteri Harjulehto, Peter Hästö, Michael Růžička
      Pages 339-366
    6. Lars Diening, Petteri Harjulehto, Peter Hästö, Michael Růžička
      Pages 367-398
  5. Applications to Partial Differential Equations

    1. Front Matter
      Pages 399-399
    2. Lars Diening, Petteri Harjulehto, Peter Hästö, Michael Růžička
      Pages 401-436
    3. Lars Diening, Petteri Harjulehto, Peter Hästö, Michael Růžička
      Pages 437-481
  6. Back Matter
    Pages 483-509

About this book

Introduction

The field of variable exponent function spaces has witnessed an explosive growth in recent years. The standard reference article for basic properties is already 20 years old. Thus this self-contained monograph collecting all the basic properties of variable exponent Lebesgue and Sobolev spaces is timely and provides a much-needed accessible reference work utilizing consistent notation and terminology. Many results are also provided with new and improved proofs. The book also presents a number of applications to PDE and fluid dynamics.

Keywords

46E30, 46E35, 26D10, 31B15, 35J60, 35Q35, 76W05 Electrorheological fluids Lebesgue spaces Non-standard growth Sobolev spaces Variable exponent

Authors and affiliations

  • Lars Diening
    • 1
  • Petteri Harjulehto
    • 2
  • Peter Hästö
    • 3
  • Michael Ruzicka
    • 4
  1. 1.Institute of MathematicsLMU MunichMunichGermany
  2. 2.Dept. of Mathematics and StatisticsUniversity of HelsinkiHelsinkiFinland
  3. 3.Dept. of Mathematical SciencesUniversity of OuluOuluFinland
  4. 4.Mathematisches InstitutUniversität FreiburgFreiburgGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-18363-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-18362-1
  • Online ISBN 978-3-642-18363-8
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site