Sobolev spaces on metric measure spaces an approach based on upper gradients
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 m...
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| Otros Autores: | , , |
| Formato: | Libro electrónico |
| Idioma: | Inglés |
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Cambridge :
Cambridge University Press
2015.
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| Colección: | EBSCO Academic eBook Collection Complete.
New mathematical monographs ; 27. |
| Acceso en línea: | Conectar con la versión electrónica |
| Ver en Universidad de Navarra: | https://innopac.unav.es/record=b4252667x*spi |
| Sumario: | 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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| Descripción Física: | xii, 434 p. |
| Formato: | Forma de acceso: World Wide Web. |
| Bibliografía: | Incluye referencias bibliográficas e índice. |
| ISBN: | 9781316248607 9781316250495 9781316135914 |
