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A First Course in Sobolev Spaces
About this Title
Giovanni Leoni, Carnegie Mellon University, Pittsburgh, PA
Publication: Graduate Studies in Mathematics
Publication Year:
2009; Volume 105
ISBNs: 978-0-8218-4768-8 (print); 978-1-4704-1169-5 (online)
DOI: https://doi.org/10.1090/gsm/105
MathSciNet review: MR2527916
MSC: Primary 46E35; Secondary 26Axx, 26B30, 28A78, 46-01
Table of Contents
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Front/Back Matter
Part 1. Functions of one variable
- Chapter 1. Monotone functions
- Chapter 2. Functions of bounded pointwise variation
- Chapter 3. Absolutely continuous functions
- Chapter 4. Curves
- Chapter 5. Lebesgue–Stieltjes measures
- Chapter 6. Decreasing rearrangement
- Chapter 7. Functions of bounded variation and Sobolev functions
Part 2. Functions of several variables
- Chapter 8. Absolutely continuous functions and change of variables
- Chapter 9. Distributions
- Chapter 10. Sobolev spaces
- Chapter 11. Sobolev spaces: Embeddings
- Chapter 12. Sobolev spaces: Further properties
- Chapter 13. Functions of bounded variation
- Chapter 14. Besov spaces
- Chapter 15. Sobolev spaces: Traces
- Chapter 16. Sobolev spaces: Symmetrization
- Appendix A. Functional analysis
- Appendix B. Measures
- Appendix C. The Lebesgue and Hausdorff measures
- Appendix D. Notes
- Appendix E. Notation and list of symbols