03212nam 2200733 a 450 991078236340332120200520144314.01-281-85136-197866118513613-7643-8722-X10.1007/978-3-7643-8722-8(CKB)1000000000546262(EBL)417466(OCoLC)304564764(SSID)ssj0000317969(PQKBManifestationID)11205739(PQKBTitleCode)TC0000317969(PQKBWorkID)10295600(PQKB)10397518(DE-He213)978-3-7643-8722-8(MiAaPQ)EBC417466(Au-PeEL)EBL417466(CaPaEBR)ebr10257963(CaONFJC)MIL185136(PPN)130186333(EXLCZ)99100000000054626220090203d2008 uy 0engur|n|---|||||txtccrGradient flows[electronic resource] in metric spaces and in the space of probability measures /Luigi Ambrosio, Nicola Gigli, Giuseppe Savaré2nd ed.Basel Birkhäuser20081 online resource (339 p.)Lectures in mathematics ETH ZürichPrevious ed.: 2005.3-7643-8721-1 Includes bibliographical references and index.Notation -- 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).Devoted 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.Lectures in mathematics ETH Zürich.Measure theoryMetric spacesDifferential equations, ParabolicMonotone operatorsEvolution equations, NonlinearMeasure theory.Metric spaces.Differential equations, Parabolic.Monotone operators.Evolution equations, Nonlinear.515.42Ambrosio Luigi44009Gigli Nicola227784Savaré Giuseppe725960MiAaPQMiAaPQMiAaPQBOOK9910782363403321Gradient flows1426029UNINA