{"product_id":"sobolev-spaces-on-metric-measure-spaces-9781107092341","title":"Sobolev Spaces on Metric Measure Spaces","description":"\u003cp\u003e • Author(s): Juha Heinonen | Pekka Koskela | Nageswari Shanmugalingam\u003cbr\u003e • Publisher: Cambridge University Press\u003cbr\u003e • Publisher Imprint: Cambridge University Press\u003cbr\u003e • BISAC: Algebra - Abstract\u003c\/p\u003e\u003cp\u003eAnalysis 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.\u003c\/p\u003e","brand":"Cambridge University Press","offers":[{"title":"Hardcover","offer_id":46432967852183,"sku":"9781107092341","price":10500.0,"currency_code":"INR","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9781107092341.webp?v=1769306888","url":"https:\/\/atlanticbooks.com\/products\/sobolev-spaces-on-metric-measure-spaces-9781107092341","provider":"Atlantic Books","version":"1.0","type":"link"}