LEADER 04744nam 2200769 a 450 001 9910461831503321 005 20200520144314.0 010 $a1-283-37995-3 010 $a9786613379955 010 $a1-4008-4269-7 024 7 $a10.1515/9781400842698 035 $a(CKB)2670000000133884 035 $a(EBL)827806 035 $a(OCoLC)769343169 035 $a(SSID)ssj0000575876 035 $a(PQKBManifestationID)11396459 035 $a(PQKBTitleCode)TC0000575876 035 $a(PQKBWorkID)10553953 035 $a(PQKB)11008932 035 $a(MiAaPQ)EBC827806 035 $a(StDuBDS)EDZ0001756336 035 $a(DE-B1597)447361 035 $a(OCoLC)979582934 035 $a(DE-B1597)9781400842698 035 $a(PPN)199244979$9sudoc 035 $a(PPN)187959625 035 $a(Au-PeEL)EBL827806 035 $a(CaPaEBR)ebr10521870 035 $a(CaONFJC)MIL337995 035 $a(EXLCZ)992670000000133884 100 $a20111017d2012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aFre?chet differentiability of Lipschitz functions and porous sets in Banach spaces$b[electronic resource] /$fJoram Lindenstrauss, David Preiss, Jaroslav Tiser 205 $aCourse Book 210 $aPrinceton $cPrinceton University Press$d2012 215 $a1 online resource (436 p.) 225 1 $aAnnals of mathematics studies ;$vno. 179 300 $aDescription based upon print version of record. 311 $a0-691-15355-8 311 $a0-691-15356-6 320 $aIncludes bibliographical references and indexes. 327 $t Frontmatter -- $tContents -- $tChapter One: Introduction -- $tChapter Two: Gâteaux differentiability of Lipschitz functions -- $tChapter Three: Smoothness, convexity, porosity, and separable determination -- $tChapter Four: ?-Fréchet differentiability -- $tChapter Five: ?-null and ?n-null sets -- $tChapter Six: Férchet differentiability except for ?-null sets -- $tChapter Seven: Variational principles -- $tChapter Eight: Smoothness and asymptotic smoothness -- $tChapter Nine: Preliminaries to main results -- $tChapter Ten: Porosity, ?n- and ?-null sets -- $tChapter Eleven: Porosity and ?-Fréchet differentiability -- $tChapter Twelve: Fréchet differentiability of real-valued functions -- $tChapter Thirteen: Fréchet differentiability of vector-valued functions -- $tChapter Fourteen: Unavoidable porous sets and nondifferentiable maps -- $tChapter Fifteen: Asymptotic Fréchet differentiability -- $tChapter Sixteen: Differentiability of Lipschitz maps on Hilbert spaces -- $tBibliography -- $tIndex -- $tIndex of Notation 330 $aThis book makes a significant inroad into the unexpectedly difficult question of existence of Fréchet derivatives of Lipschitz maps of Banach spaces into higher dimensional spaces. Because the question turns out to be closely related to porous sets in Banach spaces, it provides a bridge between descriptive set theory and the classical topic of existence of derivatives of vector-valued Lipschitz functions. The topic is relevant to classical analysis and descriptive set theory on Banach spaces. The book opens several new research directions in this area of geometric nonlinear functional analysis. The new methods developed here include a game approach to perturbational variational principles that is of independent interest. Detailed explanation of the underlying ideas and motivation behind the proofs of the new results on Fréchet differentiability of vector-valued functions should make these arguments accessible to a wider audience. The most important special case of the differentiability results, that Lipschitz mappings from a Hilbert space into the plane have points of Fréchet differentiability, is given its own chapter with a proof that is independent of much of the work done to prove more general results. The book raises several open questions concerning its two main topics. 410 0$aAnnals of mathematics studies ;$vno. 179. 606 $aBanach spaces 606 $aCalculus of variations 606 $aFunctional analysis 608 $aElectronic books. 615 0$aBanach spaces. 615 0$aCalculus of variations. 615 0$aFunctional analysis. 676 $a515/.88 686 $aSI 830$2rvk 700 $aLindenstrauss$b Joram$f1936-$041187 701 $aPreiss$b David$0515729 701 $aTis?er$b Jaroslav$f1957-$0515783 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910461831503321 996 $aFréchet differentiability of Lipschitz functions and porous sets in Banach spaces$9854568 997 $aUNINA