Sobolev Spaces on Metric Measure Spaces - An Approach Based on Upper Gradients (Hardcover)

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.

General

Imprint:	Cambridge UniversityPress
Country of origin:	United Kingdom
Series:	New Mathematical Monographs
Release date:	February 2015
Authors:	Juha Heinonen • Pekka Koskela • Nageswari Shanmugalingam • Jeremy T. Tyson
Dimensions:	234 x 157 x 33mm (L x W x T)
Format:	Hardcover
Pages:	448
ISBN-13:	978-1-107-09234-1
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Complex analysis Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis
LSN:	1-107-09234-5
Barcode:	9781107092341

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