Sobolev Spaces on Metric Measure Spaces An Approach Based on Upper Gradients
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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 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 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 Poincar inequalities under Gromov-Hausdorff convergence, and the Keith-Zhong self-improvement theorem for Poincar inequalities.
Publisher Name | Cambridge University Press |
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Author Name | Hagendorf, Col |
Format | Audio |
Bisac Subject Major | MAT |
Language | NG |
Isbn 10 | 1107092345 |
Isbn 13 | 9781107092341 |
Target Age Group | min:NA, max:NA |
Series | 00027868427 |
Dimensions | 00.90" H x 00.06" L x 00.00" W |
Page Count | 448 |
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