[Download] "Sobolev Spaces on Metric Measure Spaces" by Juha Heinonen, Pekka Koskela, Nageswari Shanmugalingam & Jeremy T. Tyson * Book PDF Kindle ePub Free
eBook details
- Title: Sobolev Spaces on Metric Measure Spaces
- Author : Juha Heinonen, Pekka Koskela, Nageswari Shanmugalingam & Jeremy T. Tyson
- Release Date : January 29, 2015
- Genre: Mathematics,Books,Science & Nature,
- Pages : * pages
- Size : 19809 KB
Description
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.
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