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 ...
Read More
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.
Read Less
Add this copy of Sobolev Spaces on Metric Measure Spaces: An Approach to cart. $125.16, new condition, Sold by Ria Christie Books rated 4.0 out of 5 stars, ships from Uxbridge, MIDDLESEX, UNITED KINGDOM, published 2015 by Cambridge University Press.
Add this copy of Sobolev Spaces on Metric Measure Spaces: An Approach to cart. $164.14, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2015 by Cambridge University Press.
Add this copy of Sobolev Spaces on Metric Measure Spaces: an Approach to cart. $192.11, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 2015 by Cambridge University Press.
