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.
- 605 pages
- English
- PDF
- Available on iOS & Android
eBook - PDF
A First Course in Fractional Sobolev Spaces
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Table of contents
- Cover
- Title page
- Copyright
- Dedication
- Contents
- Preface
- Fractional Sobolev spaces in one dimension
- Fractional Sobolev spaces in one dimension
- Embeddings and interpolation
- A bit of wavelets
- Rearrangements
- Higher order fractional Sobolev spaces in one dimension
- Fractional Sobolev spaces
- Fractional Sobolev spaces
- Embeddings and interpolation
- Further properties
- Trace theory
- Symmetrization
- Higher order fractional Sobolev spaces
- Some equivalent seminorms
- Applications
- Interior regularity for the Poisson problem
- The fractional Laplacian
- Bibliography
- Index
- Back Cover
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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 1.5 million books available in our catalogue for you to explore.