LEADER 03894nam 2200685 a 450 001 9910817810403321 005 20200520144314.0 010 $a1-282-15738-8 010 $a9786612157387 010 $a1-4008-2648-9 024 7 $a10.1515/9781400826483 035 $a(CKB)1000000000788403 035 $a(EBL)457873 035 $a(OCoLC)436943847 035 $a(SSID)ssj0000102949 035 $a(PQKBManifestationID)11133165 035 $a(PQKBTitleCode)TC0000102949 035 $a(PQKBWorkID)10060896 035 $a(PQKB)11422452 035 $a(DE-B1597)446499 035 $a(OCoLC)979910693 035 $a(DE-B1597)9781400826483 035 $a(Au-PeEL)EBL457873 035 $a(CaPaEBR)ebr10312583 035 $a(CaONFJC)MIL215738 035 $z(PPN)199244855 035 $a(PPN)164015361 035 $a(FR-PaCSA)88838061 035 $a(MiAaPQ)EBC457873 035 $a(EXLCZ)991000000000788403 100 $a20040308d2005 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAnalysis of heat equations on domains /$fEl Maati Ouhabaz 205 $aCourse Book 210 $aPrinceton, N.J. $cPrinceton University Press$dc2005 215 $a1 online resource (298 p.) 225 0 $aLondon mathematical society monograph series ;$vv. 31 300 $aDescription based upon print version of record. 311 $a0-691-12016-1 320 $aIncludes bibliographical references (p. [265]-282) and index. 327 $t Frontmatter -- $tContents -- $tPreface -- $tNotation -- $tChapter One. Sesquilinear Forms, Associated Operators, and Semigroups -- $tChapter Two. Contractivity Properties -- $tChapter Three. Inequalities for Sub-Markovian Semigroups -- $tChapter Four. Uniformly Elliptic Operators on Domains -- $tChapter Five. Degenerate-Elliptic Operators -- $tChapter Six. Gaussian Upper Bounds for Heat Kernels -- $tChapter Seven. Gaussian Upper Bounds and Lp-Spectral Theory -- $tChapter Eight. A Review of the Kato Square Root Problem -- $tBibliography -- $tIndex 330 $aThis is the first comprehensive reference published on heat equations associated with non self-adjoint uniformly elliptic operators. The author provides introductory materials for those unfamiliar with the underlying mathematics and background needed to understand the properties of heat equations. He then treats Lp properties of solutions to a wide class of heat equations that have been developed over the last fifteen years. These primarily concern the interplay of heat equations in functional analysis, spectral theory and mathematical physics. This book addresses new developments and applications of Gaussian upper bounds to spectral theory. In particular, it shows how such bounds can be used in order to prove Lp estimates for heat, Schrödinger, and wave type equations. A significant part of the results have been proved during the last decade. The book will appeal to researchers in applied mathematics and functional analysis, and to graduate students who require an introductory text to sesquilinear form techniques, semigroups generated by second order elliptic operators in divergence form, heat kernel bounds, and their applications. It will also be of value to mathematical physicists. The author supplies readers with several references for the few standard results that are stated without proofs. 410 0$aLondon Mathematical Society Monographs 606 $aHeat equation 606 $aHeat$xTransmission$xMeasurement 615 0$aHeat equation. 615 0$aHeat$xTransmission$xMeasurement. 676 $a515/.353 700 $aOuhabaz$b El Maati$0514832 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910817810403321 996 $aAnalysis of heat equations on domains$9850944 997 $aUNINA