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© 2011

Lebesgue and Sobolev Spaces with Variable Exponents

Benefits

  • First book in the area of research

  • Self-contained presentation suitable for both graduate students and researchers

  • Comprehensive book with extensive index and nomenclature

  • Applications for the developed theory is presented in the book

Book

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

  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

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Reviews

From the reviews:

“The authors provide a comprehensive survey of the state of the art concerning Lebesgue and Sobolev spaces with variable exponents. … The book is also having a rich bibliography of 399 entries, a long list of symbols and an index. It will certainly become a standard reference in this field and stimulate further work in this direction.” (H. G. Feichtinger, Monatshefte für Mathematik, Vol. 165 (1), January, 2012)

“The book is devoted to Lebesgue and Soboley spaces with variable exponents. … The present book consists of the introduction and three parts. … The majority of the results presented in the monograph were obtained by the authors and their collaborators. … the books is a useful source of unified information on Lebesgue and Soboley spaces with variable exponents.” (Alexei Yu. Karlovich, Zentralblatt MATH, Vol. 1222, 2011)

“This book consists of three parts of different lengths and intentions, sub-divided into several chapters. There is a nice figure at the very beginning of the monograph explaining the dependencies among the chapters, together with some recommendations on which parts should be used for first reading or when teaching the subject in a graduate course. … the presentation can thus also be considered as a textbook and extremely useful reference for graduate students and researchers working in related fields … .” (Dorothee D. Haroske, Mathematical Reviews, January, 2013)