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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 |
MARC
| LEADER | 00000cam a2200000 i 4500 | ||
|---|---|---|---|
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| 003 | OCoLC | ||
| 005 | 20231017213018.0 | ||
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| 020 | |a 1316248607 |q (electronic bk.) | ||
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| 020 | |z 1107092345 |q (hardback) | ||
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| 049 | |a UAMI | ||
| 100 | 1 | |a Heinonen, Juha, |e author. | |
| 245 | 1 | 0 | |a Sobolev spaces on metric measure spaces : |b an approach based on upper gradients / |c Juha Heinonen, Pekka Koskela, Nageswari Shanmugalingam, Jeremy T. Tyson. |
| 264 | 1 | |a Cambridge : |b Cambridge University Press, |c 2015. | |
| 264 | 4 | |c ©2015 | |
| 300 | |a 1 online resource (xii, 434 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a New mathematical monographs ; |v 27 | |
| 504 | |a Includes bibliographical references and indexes. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Introduction -- Review of basic functional analysis -- Lebesgue theory of Banach space-valued functions -- Lipschitz functions and embeddings -- Path integrals and modulus -- Upper gradients -- Sobolev spaces -- Poincaré inequalities -- Consequences of Poincaré inequalities -- Other definitions of Sobolev-type spaces -- Gromov-Hausdorff convergence and Poincaré inequalities -- Self-improvement of Poincaré inequalities -- An introduction to Cheeger's differentiation theory -- Examples, applications, and further research directions. | |
| 520 | |a 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. | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Metric spaces. | |
| 650 | 0 | |a Sobolev spaces. | |
| 650 | 6 | |a Espaces métriques. | |
| 650 | 6 | |a Espaces de Sobolev. | |
| 650 | 7 | |a MATHEMATICS |x Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
| 650 | 7 | |a Metric spaces |2 fast | |
| 650 | 7 | |a Sobolev spaces |2 fast | |
| 650 | 7 | |a Sobolev-Raum |2 gnd | |
| 650 | 7 | |a Metrischer Raum |2 gnd | |
| 700 | 1 | |a Heinonen, Juha, |e author. | |
| 700 | 1 | |a Koskela, Pekka, |e author. | |
| 700 | 1 | |a Shanmugalingam, Nageswari, |e author. | |
| 700 | 1 | |a Tyson, Jeremy T., |d 1972- |e author. | |
| 776 | 0 | 8 | |i Print version: |a Heinonen, Juha. |t Sobolev spaces on metric measure spaces. |d Cambridge, United Kingdom : Cambridge University Press, 2015 |z 9781107092341 |w (DLC) 2014027794 |w (OCoLC)883836458 |
| 830 | 0 | |a New mathematical monographs ; |v 27. | |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=919826 |z Texto completo |
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