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A first course in Sobolev spaces
This book is about differentiation of functions. It is divided into two parts, which can be used as different textbooks, one for an advanced undergraduate course in functions of one variable and one for a graduate course on Sobolev functions. The first part develops the theory of monotone, absolutel...
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| Auteur principal : | |
|---|---|
| Format : | Livre |
| Langue : | anglais |
| Titre complet : | A first course in Sobolev spaces / Giovanni Leoni |
| Édition : | 2nd edition |
| Publié : |
Providence (RI) :
American Mathematical Society
, copyright 2017 |
| Description matérielle : | 1 vol. (XXII-734 p.) |
| Collection : | Graduate studies in mathematics ; 181 |
| Sujets : | |
| Documents associés : | Autre format:
A first course in Sobolev spaces |
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| 200 | 1 | |a A first course in Sobolev spaces |f Giovanni Leoni | |
| 205 | |a 2nd edition | ||
| 210 | |a Providence (RI) |c American Mathematical Society |d copyright 2017 | ||
| 215 | |a 1 vol. (XXII-734 p.) |d 26 cm | ||
| 225 | 2 | |a Graduate studies in mathematics |v 181 | |
| 320 | |a Bibliogr. p. 717-728. Index | ||
| 330 | |a This book is about differentiation of functions. It is divided into two parts, which can be used as different textbooks, one for an advanced undergraduate course in functions of one variable and one for a graduate course on Sobolev functions. The first part develops the theory of monotone, absolutely continuous, and bounded variation functions of one variable and their relationship with Lebesgue Stieltjes measures and Sobolev functions. It also studies decreasing rearrangement and curves. The second edition includes a chapter on functions mapping time into Banach spaces. The second part of the book studies functions of several variables. It begins with an overview of classical results such as Rademacher's and Stepanoff's differentiability theorems, Whitney's extension theorem, Brouwer's fixed point theorem, and the divergence theorem for Lipschitz domains. It then moves to distributions, Fourier transforms and tempered distributions. [source : 4ème de couv.] | ||
| 359 | 2 | |b Chapter 1. Monotone functions |b Chapter 2. Functions of bounded pointwise variation |b Chapter 4. Decreasing rearrangement |b Chapter 5. Curves |b Chapter 6. Lebesgue-Stieltjes measures |b Chapter 7. Functions of bounded variation and Sobolev functions |b Chapter 8. Infinite-dimensional case |b Chapter 9. Change of variables and the divergence theorem |b Chapter 10. Distributions |b Chapter 11. Sobolev spaces |b Chapter 12. Sobolev spaces: Embeddings |b Chapter 13. Sobolev spaces: Further properties |b Chapter 14. Functions of bounded variation |b Chapter 15. Sobolev spaces: Symmetrization |b Chapter 16. Interpolation of Banach spaces |b Chapter 17. Besov spaces |b Chapter 18. Sobolev spaces: Traces |b Appendix A. Functional analysis |b Appendix B. Measures |b Appendix C. The Lebesgue and Hausdorff measures |b Appendix D. Notes |b Appendix E. Notation and list symbols | |
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