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Hardcover ISBN:  9781470468989 
Product Code:  GSM/229 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
Softcover ISBN:  9781470472535 
Product Code:  GSM/229.S 
List Price:  $89.00 
MAA Member Price:  $80.10 
AMS Member Price:  $71.20 
eBook ISBN:  9781470472528 
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Hardcover ISBN:  9781470468989 
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Book DetailsGraduate Studies in MathematicsVolume: 229; 2023; 586 ppMSC: 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, GagliardoNirenberg type interpolation inequalities, and trace theory. The third part explores some applications: interior regularity for the Poisson problem with the righthand 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 selfcontained.
ReadershipGraduate 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


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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, GagliardoNirenberg type interpolation inequalities, and trace theory. The third part explores some applications: interior regularity for the Poisson problem with the righthand 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 selfcontained.
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