000			03054nam a22004098i 4500
001			CR9781316135914
003			UkCbUP
005			20200124160213.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			140611s2015||||enk o ||1 0|eng|d
020			_a9781316135914 (ebook)
020			_z9781107092341 (hardback)
020			_z9781107465343 (paperback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	4	_aQA611.28 _b.H45 2015
082	0	0	_a515/.7 _223
100	1		_aHeinonen, Juha, _eauthor.
245	1	0	_aSobolev spaces on metric measure spaces : _ban approach based on upper gradients / _cJuha Heinonen, Pekka Koskela, Nageswari Shanmugalingam, Jeremy T. Tyson.
264		1	_aCambridge : _bCambridge University Press, _c2015.
300			_a1 online resource (xii, 434 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aNew mathematical monographs ; _v27
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0		_aIntroduction -- 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			_aAnalysis 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	_aMetric spaces.
650		0	_aSobolev spaces.
700	1		_aKoskela, Pekka, _eauthor.
700	1		_aShanmugalingam, Nageswari, _eauthor.
700	1		_aTyson, Jeremy T., _d1972- _eauthor.
776	0	8	_iPrint version: _z9781107092341
830		0	_aNew mathematical monographs ; _v27.
856	4	0	_uhttps://doi.org/10.1017/CBO9781316135914
999			_c516038 _d516036