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A First Course in Sobolev Spaces: Second Edition
About this Title
Giovanni Leoni, Carnegie Mellon University, Pittsburgh, PA
Publication: Graduate Studies in Mathematics
Publication Year:
2017; Volume 181
ISBNs: 978-1-4704-2921-8 (print); 978-1-4704-4226-2 (online)
DOI: https://doi.org/10.1090/gsm/181
MathSciNet review: MR3726909
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
- Monotone functions
- Functions of bounded pointwise variation
- Absolutely continuous functions
- Decreasing rearrangement
- Curves
- Lebesgue–Stieltjes measures
- Functions of bounded variation and Sobolev functions
- The infinite-dimensional case
Part 2. Functions of several variables
- Change of variables and the divergence theorem
- Distributions
- Sobolev spaces
- Sobolev spaces: Embeddings
- Sobolev spaces: Further properties
- Functions of bounded variation
- Sobolev spaces: Symmetrization
- Interpolation of Banach spaces
- Besov spaces
- Sobolev spaces: Traces
- Appendix A. Functional analysis
- Appendix B. Measures
- Appendix C. The Lebesgue and Hausdorff measures
- Appendix D. Notes
- Appendix E. Notation and list of symbols