Eulerian calculus for the displacement convexity in the wasserstein distance
Daneri S, Savaré G (2008)
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 2008
Journal
Publisher: Society for Industrial and Applied Mathematics
Book Volume: 40
Pages Range: 1104-1122
Journal Issue: 3
DOI: 10.1137/08071346X
Abstract
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. © 2008 Society for Industrial and Applied Mathematics.
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APA:
Daneri, S., & Savaré, G. (2008). Eulerian calculus for the displacement convexity in the wasserstein distance. SIAM Journal on Mathematical Analysis, 40(3), 1104-1122. https://dx.doi.org/10.1137/08071346X
MLA:
Daneri, Sara, and Giuseppe Savaré. "Eulerian calculus for the displacement convexity in the wasserstein distance." SIAM Journal on Mathematical Analysis 40.3 (2008): 1104-1122.
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