Sobolev spaces on metric measure spaces : (Record no. 516038)
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| 000 -LEADER | |
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| fixed length control field | 03054nam a22004098i 4500 |
| 001 - CONTROL NUMBER | |
| control field | CR9781316135914 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | UkCbUP |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20200124160213.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS--GENERAL INFORMATION | |
| fixed length control field | m|||||o||d|||||||| |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr|||||||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 140611s2015||||enk o ||1 0|eng|d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781316135914 (ebook) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Cancelled/invalid ISBN | 9781107092341 (hardback) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Cancelled/invalid ISBN | 9781107465343 (paperback) |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | UkCbUP |
| Language of cataloging | eng |
| Description conventions | rda |
| Transcribing agency | UkCbUP |
| 050 04 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA611.28 |
| Item number | .H45 2015 |
| 082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 515/.7 |
| Edition number | 23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Heinonen, Juha, |
| Relator term | author. |
| 245 10 - TITLE STATEMENT | |
| Title | Sobolev spaces on metric measure spaces : |
| Remainder of title | an approach based on upper gradients / |
| Statement of responsibility, etc | Juha Heinonen, Pekka Koskela, Nageswari Shanmugalingam, Jeremy T. Tyson. |
| 264 #1 - Production, Publication, Distribution, Manufacture, and Copyright Notice (R) | |
| Place of production, publication, distribution, manufacture (R) | Cambridge : |
| Name of producer, publisher, distributor, manufacturer (R) | Cambridge University Press, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2015. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (xii, 434 pages) : |
| Other physical details | digital, PDF file(s). |
| 336 ## - Content Type (R) | |
| Content type term (R) | text |
| Content type code (R) | txt |
| Source (NR) | rdacontent |
| 337 ## - Media Type (R) | |
| Media type term (R) | computer |
| Media type code (R) | c |
| Source (NR) | rdamedia |
| 338 ## - Carrier Type (R) | |
| Carrier type term (R) | online resource |
| Carrier type code (R) | cr |
| Source (NR) | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| სერიის ცნობა | New mathematical monographs ; |
| Volume number/sequential designation | 27 |
| 500 ## - GENERAL NOTE | |
| General note | Title from publisher's bibliographic system (viewed on 05 Oct 2015). |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 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 ## - SUMMARY, ETC. | |
| Summary, etc | 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. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Metric spaces. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Sobolev spaces. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Koskela, Pekka, |
| Relator term | author. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Shanmugalingam, Nageswari, |
| Relator term | author. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Tyson, Jeremy T., |
| Dates associated with a name | 1972- |
| Relator term | author. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Display text | Print version: |
| International Standard Book Number | 9781107092341 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | New mathematical monographs ; |
| Volume number/sequential designation | 27. |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://doi.org/10.1017/CBO9781316135914">https://doi.org/10.1017/CBO9781316135914</a> |
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