{"product_id":"sobolev-spaces-on-metric-measure-juha-heinonen-9781107092341","title":"Sobolev Spaces on Metric Measure Spaces","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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Juha Heinonen,Pekka Koskela,Nageswari Shanmugalingam\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 1107092345\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9781107092341\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Cambridge University Press\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 02\/05\/2015\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 448\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.82lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.00h x 6.00w x 1.13d","brand":"Juha Heinonen","offers":[{"title":"Hardcover","offer_id":48449263337727,"sku":"9781107092341","price":170.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_124f06b9-89b7-4d79-89a2-67d3446c7ab6.jpg?v=1777262616","url":"https:\/\/www.whiterainbookhouse.com\/products\/sobolev-spaces-on-metric-measure-juha-heinonen-9781107092341","provider":"WR Book House","version":"1.0","type":"link"}