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Sobolev Spaces on Metric Measure Spaces

Sobolev Spaces on Metric Measure Spaces An Approach Based on Upper Gradients - New Mathematical Monographs

Hardback (02 May 2015)

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Publisher's 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.

About the Publisher

Cambridge University Press

Cambridge University Press dates from 1534 and is part of the University of Cambridge. We further the University's mission by disseminating knowledge in the pursuit of education, learning and research at the highest international levels of excellence.

Book information

ISBN: 9781107092341
Publisher: Cambridge University Press
Imprint: Cambridge University Press
Pub date:
DEWEY: 515.7
DEWEY edition: 23
Language: English
Number of pages: 448
Weight: 650g
Height: 234mm
Width: 157mm
Spine width: 33mm