LEADER 04914nam 22007454a 450 001 9910811320303321 005 20200520144314.0 010 $a1-107-11991-X 010 $a1-280-42958-5 010 $a9786610429585 010 $a0-511-17727-5 010 $a0-511-15823-8 010 $a0-511-32567-3 010 $a0-511-54321-2 010 $a0-511-04995-1 035 $a(CKB)1000000000007129 035 $a(EBL)201669 035 $a(OCoLC)56125251 035 $a(SSID)ssj0000242859 035 $a(PQKBManifestationID)11923085 035 $a(PQKBTitleCode)TC0000242859 035 $a(PQKBWorkID)10311555 035 $a(PQKB)11306158 035 $a(UkCbUP)CR9780511543210 035 $a(Au-PeEL)EBL201669 035 $a(CaPaEBR)ebr10023388 035 $a(Au-PeEL)EBL4949597 035 $a(CaONFJC)MIL42958 035 $a(OCoLC)1024261049 035 $a(MiAaPQ)EBC201669 035 $a(MiAaPQ)EBC4949597 035 $a(PPN)261308262 035 $a(EXLCZ)991000000000007129 100 $a20020212d2002 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aSecond order partial differential equations in Hilbert spaces /$fGiuseppe Da Prato, Jerzy Zabczyk 205 $a1st ed. 210 $aCambridge, UK ;$aNew York $cCambridge University Press$d2002 215 $a1 online resource (xvi, 379 pages) $cdigital, PDF file(s) 225 1 $aLondon Mathematical Society lecture note series ;$v293 300 $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015). 311 $a0-511-04086-5 311 $a0-521-77729-1 320 $aIncludes bibliographical references (p. 358-375) and index. 327 $tTheory in Spaces of Continuous Functions --$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. 330 $aSecond order linear parabolic and elliptic equations arise frequently in mathematics and other disciplines. For example parabolic equations are to be found in statistical mechanics and solid state theory, their infinite dimensional counterparts are important in fluid mechanics, mathematical finance and population biology, whereas nonlinear parabolic equations arise in control theory. Here the authors present a state of the art treatment of the subject from a new perspective. The main tools used are probability measures in Hilbert and Banach spaces and stochastic evolution equations. There is then a discussion of how the results in the book can be applied to control theory. This area is developing very rapidly and there are numerous notes and references that point the reader to more specialised results not covered in the book. Coverage of some essential background material will help make the book self-contained and increase its appeal to those entering the subject. 410 0$aLondon Mathematical Society lecture note series ;$v293. 606 $aDifferential equations, Partial 606 $aHilbert space 615 0$aDifferential equations, Partial. 615 0$aHilbert space. 676 $a515/.353 700 $aDa Prato$b Giuseppe$0314271 701 $aZabczyk$b Jerzy$041807 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910811320303321 996 $aSecond order partial differential equations in Hilbert spaces$91458203 997 $aUNINA