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Hardcover ISBN: | 978-1-4704-6898-9 |
Product Code: | GSM/229 |
List Price: | $135.00 |
MAA Member Price: | $121.50 |
AMS Member Price: | $108.00 |
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 |
Hardcover ISBN: | 978-1-4704-6898-9 |
eBook ISBN: | 978-1-4704-7252-8 |
Product Code: | GSM/229.B |
List Price: | $220.00 $177.50 |
MAA Member Price: | $198.00 $159.75 |
AMS Member Price: | $176.00 $142.00 |
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 |
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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, 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.
ReadershipGraduate students and researchers interested in fractional Sobolev spaces.
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Table of Contents
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Fractional Sobolev spaces in one dimension
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Fractional Sobolev spaces in one dimension
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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
-
-
Additional Material
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RequestsReview Copy – for publishers of book reviewsDesk Copy – for instructors who have adopted an AMS textbook for a courseExamination Copy – for faculty considering an AMS textbook for a courseAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Requests
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.
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