Cargando…
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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
2015.
|
| Colección: | New mathematical monographs ;
27. |
| Temas: | |
| Acceso en línea: | Texto completo |
| 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. |
|---|---|
| Descripción Física: | 1 online resource (xii, 434 pages) |
| Bibliografía: | Includes bibliographical references and indexes. |
| ISBN: | 9781316248607 1316248607 9781316250495 1316250490 9781316135914 1316135918 |