期刊
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
卷 40, 期 3, 页码 1104-1122出版社
SIAM PUBLICATIONS
DOI: 10.1137/08071346X
关键词
gradient flows; displacement convexity; heat and porous medium equation; nonlinear diffusion; optimal transport; Kantorovich-Rubinstein-Wasserstein distance; Riemannian manifolds with a lower Ricci curvature bound
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.
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