02268nam 2200457 450 991079407970332120200410120640.01-4704-5513-7(CKB)4100000010348440(MiAaPQ)EBC6118470(RPAM)21609892(PPN)245283226(EXLCZ)99410000001034844020200410d2019 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierNonlinear diffusion equations and curvature conditions in metric measure spaces /Luigi Ambrosio, Andrea Mondino, Giuseppe SavaréProvidence, Rhode Island :American Mathematical Society,[2019]©20191 online resource (v, 121 pages) illustrationsMemoirs of the American Mathematical Society ;Number 12701-4704-3913-1 Includes bibliographical references.Contraction and convexity via Hamiltonian estimates : an heuristic argument -- Dirichlet forms, homogeneous spaces and nonlinear diffusion -- Backward and forward linearizations of nonlinear diffusion -- Preliminaries -- Absolutely continuous curves in Wasserstein spaces and continuity inequalities in a metric setting -- Weighted energy functionals along absolutely continuous curves -- Dynamic Kantorovich potentials, continuity equation and dual weighted Cheeger energies -- The RCD* (K, N) condition and its characterizations through weighted convexity and evolution variational inequalities -- The Bakry-Émery condition -- Nonlinear diffusion equations and action estimates -- The equivalence between BE(K, N) and RCD* (K, N).Memoirs of the American Mathematical Society ;Number 1270.Metric spacesMetric spaces.514.3249J5249Q2035K5558J3535K9031C2558B20mscAmbrosio Luigi44009Mondino AndreaMiAaPQMiAaPQMiAaPQBOOK9910794079703321Nonlinear diffusion equations and curvature conditions in metric measure spaces3699793UNINA