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We present a short overview on the strongest variational formulation for gradient flows of geodesically $\lambda$-convex functionals in metric spaces, with applications to diffusion equations in Wasserstein spaces of probability measures.
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Richard Jordan, David Kinderlehrer, and Felix Otto · 1998
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Contractivity of Wasserstein metrics and asymptotic profiles for scalar conservation laws
José A. Carrillo, Marco Di Francesco, and Corrado Lattanzio · 2006
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Contractions in the 2-Wasserstein length space and thermalization of granular media
José A. Carrillo, Robert J. McCann, and Cédric Villani · 2006
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On the geometry of metric measure spaces. I
Karl-Theodor Sturm · 2006
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Shin-ichi Ohta · 2007
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Ricardo H. Nochetto, Giuseppe Savaré, and Claudio Verdi · 2000
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Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
F. Otto and C. Villani · 2000
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A course in metric geometry
Dmitri Burago, Yuri Burago, and Sergei Ivanov · 2001
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Eulerian calculus for the displacement convexity in the Wasserstein distance
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Wasserstein space over the wiener space
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Existence and stability for Fokker-Planck equations with log-concave reference measure
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Introduction to gradient flows in metric spaces
Philippe Clément · 2009
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Ricci curvature for metric-measure spaces via optimal transport
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A family of nonlinear fourth order equations of gradient flow type
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Luca Natile and Giuseppe Savarè · 2009
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Gradient flows on Wasserstein spaces over compact Alexandrov spaces
Shin-ichi Ohta · 2009
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Optimal transport. Old and new
Cédric Villani · 2009
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Nonlinear mobility continuity equations and generalized displacement convexity
J. A. Carrillo, S. Lisini, G. Savaré, and D. Slepcev · 2010
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