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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Sobolev Spaces on Metric Measure Spaces

Sobolev Spaces on Metric Measure Spaces

Heinonen, Juha
Koskela, Pekka
Shanmugalingam, Nageswari

Hardcover

Series: New Mathematical Monographs, Book 27

AlgebraCalculus

ISBN10: 1107092345
ISBN13: 9781107092341
Publisher: Cambridge University Press
Published: Feb 5 2015
Pages: 448
Weight: 1.82
Height: 1.13 Width: 6.00 Depth: 9.00
Language: English
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.

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