Sobolev spaces on metric measure spaces an approach based on upper gradients
Analysis on metric spaces emerged in the 1990s as an independent research field providing a unified treatment of first-order analysis in diverse and potentially nonsmooth settings. Based on the fundamental concept of upper gradient, the notion of a Sobolev function was formulated in the setting of m...
| Main Authors: | , , , |
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| Format: | eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2015
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| Series: | New mathematical monographs
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| Subjects: | |
| Online Access: | |
| Collection: | Cambridge Books Online - Collection details see MPG.ReNa |
Table of Contents:
- Introduction
- Review of basic functional analysis
- Lebesgue theory of Banach space-valued functions
- Lipschitz functions and embeddings
- Path integrals and modulus
- Upper gradients
- Sobolev spaces
- Poincaré inequalities
- Consequences of Poincaré inequalities
- Other definitions of Sobolev-type spaces
- Gromov-Hausdorff convergence and Poincaré inequalities
- Self-improvement of Poincaré inequalities
- An introduction to Cheeger's differentiation theory
- Examples, applications, and further research directions