Volume 2017 2011

Lebesgue and Sobolev Spaces with Variable Exponents

ISBN: 978-3-642-18362-1 (Print) 978-3-642-18363-8 (Online)

Table of contents (14 chapters)

  1. Front Matter

    Pages i-ix

  2. No Access

    Book Chapter

    Pages 1-17

    Introduction

  3. Lebesgue spaces

    1. Front Matter

      Pages 19-19

    2. No Access

      Book Chapter

      Pages 21-68

      A Framework for Function Spaces

    3. No Access

      Book Chapter

      Pages 69-97

      Variable Exponent Lebesgue Spaces

    4. No Access

      Book Chapter

      Pages 99-141

      The Maximal Operator

    5. No Access

      Book Chapter

      Pages 143-197

      The Generalized Muckenhoupt Condition*

    6. No Access

      Book Chapter

      Pages 199-212

      Classical Operators

    7. No Access

      Book Chapter

      Pages 213-244

      Transfer Techniques

  4. Sobolev spaces

    1. Front Matter

      Pages 245-245

    2. No Access

      Book Chapter

      Pages 247-288

      Introduction to Sobolev Spaces

    3. No Access

      Book Chapter

      Pages 289-314

      Density of Regular Functions

    4. No Access

      Book Chapter

      Pages 315-338

      Capacities

    5. No Access

      Book Chapter

      Pages 339-366

      Fine Properties of Sobolev Functions

    6. No Access

      Book Chapter

      Pages 367-398

      Other Spaces of Differentiable Functions

  5. Applications to partial differential equations

    1. Front Matter

      Pages 399-399

    2. No Access

      Book Chapter

      Pages 401-436

      Dirichlet Energy Integral and Laplace Equation

    3. No Access

      Book Chapter

      Pages 437-481

      PDEs and Fluid Dynamics

  6. Back Matter

    Pages 483-509