A First Course in Fractional Sobolev Spaces
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A First Course in Fractional Sobolev Spaces

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eBook - PDF

A First Course in Fractional Sobolev Spaces

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About This Book

This book provides a gentle introduction to fractional Sobolev spaces which play a central role in the calculus of variations, partial differential equations, and harmonic analysis. The first part deals with fractional Sobolev spaces of one variable. It covers the definition, standard properties, extensions, embeddings, Hardy inequalities, and interpolation inequalities. The second part deals with fractional Sobolev spaces of several variables. The author studies completeness, density, homogeneous fractional Sobolev spaces, embeddings, necessary and sufficient conditions for extensions, Gagliardo-Nirenberg type interpolation inequalities, and trace theory. The third part explores some applications: interior regularity for the Poisson problem with the right-hand side in a fractional Sobolev space and some basic properties of the fractional Laplacian.The first part of the book is accessible to advanced undergraduates with a strong background in integration theory; the second part, to graduate students having familiarity with measure and integration and some functional analysis. Basic knowledge of Sobolev spaces would help, but is not necessary. The book can also serve as a reference for mathematicians working in the calculus of variations and partial differential equations as well as for researchers in other disciplines with a solid mathematics background. It contains several exercises and is self-contained.

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Yes, you can access A First Course in Fractional Sobolev Spaces by Giovanni Leoni in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematics General. We have over one million books available in our catalogue for you to explore.

Information

Publisher
American Mathematical Society
Year
2023
ISBN
9781470472528
Topic
Mathematics
Subtopic
Mathematics General
Index
Mathematics

Table of contents

  1. Cover
  2. Title page
  3. Copyright
  4. Dedication
  5. Contents
  6. Preface
  7. Fractional Sobolev spaces in one dimension
  8. Fractional Sobolev spaces in one dimension
  9. Embeddings and interpolation
  10. A bit of wavelets
  11. Rearrangements
  12. Higher order fractional Sobolev spaces in one dimension
  13. Fractional Sobolev spaces
  14. Fractional Sobolev spaces
  15. Embeddings and interpolation
  16. Further properties
  17. Trace theory
  18. Symmetrization
  19. Higher order fractional Sobolev spaces
  20. Some equivalent seminorms
  21. Applications
  22. Interior regularity for the Poisson problem
  23. The fractional Laplacian
  24. Bibliography
  25. Index
  26. Back Cover