000			03902nam a22003738i 4500
001			CR9780511543210
003			UkCbUP
005			20200124160240.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			090505s2002||||enk o ||1 0|eng|d
020			_a9780511543210 (ebook)
020			_z9780521777292 (paperback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA374 _b.D27 2002
082	0	0	_a515/.353 _221
100	1		_aDa Prato, Giuseppe, _eauthor.
245	1	0	_aSecond order partial differential equations in Hilbert spaces / _cGiuseppe Da Prato, Jerzy Zabczyk.
264		1	_aCambridge : _bCambridge University Press, _c2002.
300			_a1 online resource (xvi, 379 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aLondon Mathematical Society lecture note series ; _v293
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0	0	_tTheory in Spaces of Continuous Functions -- _tGaussian measures -- _tIntroduction and preliminaries -- _tDefinition and first properties of Gaussian measures -- _tMeasures in metric spaces -- _tGaussian measures -- _tComputation of some Gaussian integrals -- _tThe reproducing kernel -- _tAbsolute continuity of Gaussian measures -- _tEquivalence of product measures in R[superscript [infinity] -- _tThe Cameron-Martin formula -- _tThe Feldman-Hajek theorem -- _tBrownian motion -- _tSpaces of continuous functions -- _tPreliminary results -- _tApproximation of continuous functions -- _tInterpolation spaces -- _tInterpolation between UC[subscript b](H) and UC[superscript 1 subscript b](H) -- _tInterpolatory estimates -- _tAdditional interpolation results -- _tThe heat equation -- _tStrict solutions -- _tRegularity of generalized solutions -- _tQ-derivatives -- _tQ-derivatives of generalized solutions -- _tComments on the Gross Laplacian -- _tThe heat semigroup and its generator -- _tPoisson's equation -- _tExistence and uniqueness results -- _tRegularity of solutions -- _tThe equation [Delta subscript Q]u = g -- _tThe Liouville theorem -- _tElliptic equations with variable coefficients -- _tSmall perturbations -- _tLarge perturbations -- _tOrnstein-Uhlenbeck equations -- _tExistence and uniqueness of strict solutions -- _tClassical solutions -- _tThe Ornstein-Uhlenbeck semigroup -- _t[pi]-Convergence -- _tProperties of the [pi]-semigroup (R[subscript t]) -- _tThe infinitesimal generator -- _tElliptic equations -- _tSchauder estimates -- _tThe Liouville theorem -- _tPerturbation results for parabolic equations.
520			_aSecond order linear parabolic and elliptic equations arise frequently in mathematics and other disciplines. For example parabolic equations are to be found in statistical mechanics and solid state theory, their infinite dimensional counterparts are important in fluid mechanics, mathematical finance and population biology, whereas nonlinear parabolic equations arise in control theory. Here the authors present a state of the art treatment of the subject from a new perspective. The main tools used are probability measures in Hilbert and Banach spaces and stochastic evolution equations. There is then a discussion of how the results in the book can be applied to control theory. This area is developing very rapidly and there are numerous notes and references that point the reader to more specialised results not covered in the book. Coverage of some essential background material will help make the book self-contained and increase its appeal to those entering the subject.
650		0	_aDifferential equations, Partial.
650		0	_aHilbert space.
700	1		_aZabczyk, Jerzy, _eauthor.
776	0	8	_iPrint version: _z9780521777292
830		0	_aLondon Mathematical Society lecture note series ; _v293.
856	4	0	_uhttps://doi.org/10.1017/CBO9780511543210
999			_c518416 _d518414