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A First Course in Fractional Sobolev Spaces
 
Giovanni Leoni Carnegie Mellon University, Pittsburgh, PA
Softcover ISBN:  978-1-4704-7253-5
Product Code:  GSM/229.S
List Price: $89.00
MAA Member Price: $80.10
AMS Member Price: $71.20
eBook ISBN:  978-1-4704-7252-8
Product Code:  GSM/229.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-7253-5
eBook: ISBN:  978-1-4704-7252-8
Product Code:  GSM/229.S.B
List Price: $174.00 $131.50
MAA Member Price: $156.60 $118.35
AMS Member Price: $139.20 $105.20
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A First Course in Fractional Sobolev Spaces
Giovanni Leoni Carnegie Mellon University, Pittsburgh, PA
Softcover ISBN:  978-1-4704-7253-5
Product Code:  GSM/229.S
List Price: $89.00
MAA Member Price: $80.10
AMS Member Price: $71.20
eBook ISBN:  978-1-4704-7252-8
Product Code:  GSM/229.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-7253-5
eBook ISBN:  978-1-4704-7252-8
Product Code:  GSM/229.S.B
List Price: $174.00 $131.50
MAA Member Price: $156.60 $118.35
AMS Member Price: $139.20 $105.20
  • Book Details
     
     
    Graduate Studies in Mathematics
    Volume: 2292023; 586 pp
    MSC: Primary 46; Secondary 26; 30; 35

    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.

    Readership

    Graduate students and researchers interested in fractional Sobolev spaces.

  • Table of Contents
     
     
    • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Examination Copy – for faculty considering an AMS textbook for a course
    Accessibility – to request an alternate format of an AMS title
Volume: 2292023; 586 pp
MSC: Primary 46; Secondary 26; 30; 35

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.

Readership

Graduate students and researchers interested in fractional Sobolev spaces.

  • 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
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Accessibility – to request an alternate format of an AMS title
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