{"product_id":"9781107092341","title":"Sobolev Spaces on Metric Measure Spaces : An Approach Based on Upper Gradients (New Mathematical Monographs)","description":"\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":"Default Title","offer_id":52301056475447,"sku":"00000_00000_00000_00000","price":969.82,"currency_code":"MYR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0962\/3548\/7543\/files\/9781107092341-1.jpg?v=1783150613","url":"https:\/\/kinokuniya.com.my\/products\/9781107092341","provider":"Books Kinokuniya Malaysia","version":"1.0","type":"link"}