TY - CHAP
T1 - Lecture notes on gradient flows and optimal transport
Y1 - 2014
A1 - Sara Daneri
A1 - Giuseppe Savarè
AB - We present a short overview on the strongest variational formulation for gradient flows of geodesically λ-convex functionals in metric spaces, with applications to diffusion equations in Wasserstein spaces of probability measures. These notes are based on a series of lectures given by the second author for the Summer School "Optimal transportation: Theory and applications" in Grenoble during the week of June 22-26, 2009.
PB - Cambridge University Press
UR - http://urania.sissa.it/xmlui/handle/1963/35093
N1 - Book title: Optimal transportation
U1 - 35348
U2 - Mathematics
U4 - 1
ER -
TY - JOUR
T1 - Eulerian calculus for the displacement convexity in the Wasserstein distance
JF - SIAM J. Math. Anal. 40 (2008) 1104-1122
Y1 - 2008
A1 - Sara Daneri
A1 - Giuseppe Savarè
AB - In this paper we give a new proof of the (strong) displacement convexity of a class of integral functionals defined on a compact Riemannian manifold satisfying a lower Ricci curvature bound. Our approach does not rely on existence and regularity results for optimal transport maps on Riemannian manifolds, but it is based on the Eulerian point of view recently introduced by Otto and Westdickenberg [SIAM J. Math. Anal., 37 (2005), pp. 1227-1255] and on the metric characterization of the gradient flows generated by the functionals in the Wasserstein space.
PB - SIAM
UR - http://hdl.handle.net/1963/3413
U1 - 922
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -