A First Course in Fractional Sobolev Spaces
Seiten
2023
American Mathematical Society (Verlag)
978-1-4704-6898-9 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-6898-9 (ISBN)
- Titel ist leider vergriffen;
keine Neuauflage - Artikel merken
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 book can serve as a reference for mathematicians working in the calculus of variations and partial differential equations as well as for researchers in other disciplines.
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.
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.
Giovanni Leoni, Carnegie Mellon University, Pittsburgh, PA.
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
| Erscheinungsdatum | 09.01.2023 |
|---|---|
| Reihe/Serie | Graduate Studies in Mathematics |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 554 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-10 | 1-4704-6898-0 / 1470468980 |
| ISBN-13 | 978-1-4704-6898-9 / 9781470468989 |
| Zustand | Neuware |
| Haben Sie eine Frage zum Produkt? |
Mehr entdecken
aus dem Bereich
aus dem Bereich
Buch | Softcover (2024)
De Gruyter Oldenbourg (Verlag)
CHF 83,90
