Sobolev spaces on metric measure spaces

✍ Scribed by Heinonen J., Koskela P., Shanmugalingam N., Tyson J.T.

Publisher: Cambridge University Press
Year: 2015
Tongue: English
Leaves: 448
Series: New mathematical monographs 27
Category: Library

No coin nor oath required. For personal study only.

✦ Table of Contents

Content: Preface
1. Introduction
2. Review of basic functional analysis
3. Lebesgue theory of Banach space-valued functions
4. Lipschitz functions and embeddings
5. Path integrals and modulus
6. Upper gradients
7. Sobolev spaces
8. Poincare inequalities
9. Consequences of Poincare inequalities
10. Other definitions of Sobolev-type spaces
11. Gromov-Hausdorff convergence and Poincare inequalities
12. Self-improvement of Poincare inequalities
13. An Introduction to Cheeger's differentiation theory
14. Examples, applications and further research directions
References
Notation index
Subject index.

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