Sobolev Spaces on Metric Measure Spaces: An Approach Based on Upper Gradients: 27 (New Mathematical Monographs, Series Number 27) - Image 1

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Cambridge University Press Sobolev Spaces on Metric Measure Spaces: An Approach Based on Upper Gradients: 27 (New Mathematical Monographs, Series Number 27)

Name: Sobolev Spaces on Metric Measure Spaces: An Approach Based on Upper Gradients: 27 (New Mathematical Monographs, Series Number 27)
Brand: Cambridge University Press
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Functional Analysis

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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.

Product Specifications

Brand: Cambridge University Press
Format: hardcover
ASIN: 1107092345
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Mathematical Analysis > Functional Analysis
Domain: Amazon UK
Release Date: 05 February 2015
Listed Since: 28 June 2014

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Cambridge University Press Sobolev Spaces on Metric Measure Spaces: An Approach Based on Upper Gradients: 27 (New Mathematical Monographs, Series Number 27)

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