Sobolev Spaces on Metric Measure Spaces An Approach Based on Upper Gradients
Sobolev Spaces on Metric Measure SpacesAn Approach Based on Upper Gradients\nAuthor(s): Juha Heinonen, Pekka Koskela, Nageswari Shanmugalingam, Jeremy T. Tyson\nFormat: Hardback\nPublisher: Cambridge University Press, United Kingdom\nImprint: Cambridge University Press\nISBN-13: 9781107092341, 978-1107092341\nSynopsis\nAnalysis 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 Poincar 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 Poincar inequality, and indicates numerous examp.
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