Sobolev Spaces on Metric Measure Spaces (BOK)

Juha Heinonen

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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 Poincare 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 Poincare 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 Poincare inequalities under Gromov-Hausdorff convergence, and the Keith-Zhong self-improvement theorem for Poincare inequalities.


Språk Engelsk Engelsk Innbinding Innbundet
Utgitt 2015 Forfatter Juha Heinonen
ISBN 9781107092341
Antall sider 465 Dimensjoner 15,8cm x 23,6cm x 3,3cm
Vekt 832 gram Leverandør Bertram Trading Ltd