Sobolev Spaces on Metric Measure Spaces: An Approach Based on Upper Gradients
By: and and and
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- Synopsis
- 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 metric measure spaces supporting a Poincaré inequality. This coherent treatment from first principles is an ideal introduction to the subject for graduate students and a useful reference for experts. It presents the foundations of the theory of such first-order Sobolev spaces, then explores geometric implications of the critical Poincaré inequality, and indicates numerous examples of spaces satisfying this axiom. A distinguishing feature of the book is its focus on vector-valued Sobolev spaces. The final chapters include proofs of several landmark theorems, including Cheeger's stability theorem for Poincaré inequalities under Gromov-Hausdorff convergence, and the Keith-Zhong self-improvement theorem for Poincaré inequalities.
- Copyright:
- 2013
Book Details
- Book Quality:
- Publisher Quality
- ISBN-13:
- 9781316235362
- Publisher:
- Cambridge University Press
- Date of Addition:
- 01/27/15
- Copyrighted By:
- Pekka Koskela, Nageswari Shanmugalingam Juha Heinonen, Jeremy T. Tyson
- Adult content:
- No
- Language:
- English
- Has Image Descriptions:
- No
- Categories:
- Nonfiction, Mathematics and Statistics
- Submitted By:
- Bookshare Staff
- Usage Restrictions:
- This is a copyrighted book.
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