LEADER 03212nam 2200733 a 450 001 9910782363403321 005 20200520144314.0 010 $a1-281-85136-1 010 $a9786611851361 010 $a3-7643-8722-X 024 7 $a10.1007/978-3-7643-8722-8 035 $a(CKB)1000000000546262 035 $a(EBL)417466 035 $a(OCoLC)304564764 035 $a(SSID)ssj0000317969 035 $a(PQKBManifestationID)11205739 035 $a(PQKBTitleCode)TC0000317969 035 $a(PQKBWorkID)10295600 035 $a(PQKB)10397518 035 $a(DE-He213)978-3-7643-8722-8 035 $a(MiAaPQ)EBC417466 035 $a(Au-PeEL)EBL417466 035 $a(CaPaEBR)ebr10257963 035 $a(CaONFJC)MIL185136 035 $a(PPN)130186333 035 $a(EXLCZ)991000000000546262 100 $a20090203d2008 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aGradient flows$b[electronic resource] $ein metric spaces and in the space of probability measures /$fLuigi Ambrosio, Nicola Gigli, Giuseppe Savare? 205 $a2nd ed. 210 $aBasel $cBirkha?user$d2008 215 $a1 online resource (339 p.) 225 1 $aLectures in mathematics ETH Zu?rich 300 $aPrevious ed.: 2005. 311 $a3-7643-8721-1 320 $aIncludes bibliographical references and index. 327 $aNotation -- Notation -- Gradient Flow in Metric Spaces -- Curves and Gradients in Metric Spaces -- Existence of Curves of Maximal Slope and their Variational Approximation -- Proofs of the Convergence Theorems -- Uniqueness, Generation of Contraction Semigroups, Error Estimates -- Gradient Flow in the Space of Probability Measures -- Preliminary Results on Measure Theory -- The Optimal Transportation Problem -- The Wasserstein Distance and its Behaviour along Geodesics -- Absolutely Continuous Curves in p(X) and the Continuity Equation -- Convex Functionals in p(X) -- Metric Slope and Subdifferential Calculus in (X) -- Gradient Flows and Curves of Maximal Slope in p(X). 330 $aDevoted to a theory of gradient flows in spaces which are not necessarily endowed with a natural linear or differentiable structure, this book focuses on gradient flows in metric spaces. It covers gradient flows in the space of probability measures on a separable Hilbert space, endowed with the Kantorovich-Rubinstein-Wasserstein distance. 410 0$aLectures in mathematics ETH Zu?rich. 606 $aMeasure theory 606 $aMetric spaces 606 $aDifferential equations, Parabolic 606 $aMonotone operators 606 $aEvolution equations, Nonlinear 615 0$aMeasure theory. 615 0$aMetric spaces. 615 0$aDifferential equations, Parabolic. 615 0$aMonotone operators. 615 0$aEvolution equations, Nonlinear. 676 $a515.42 700 $aAmbrosio$b Luigi$044009 701 $aGigli$b Nicola$0227784 701 $aSavare?$b Giuseppe$0725960 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910782363403321 996 $aGradient flows$91426029 997 $aUNINA