Euler–Poisson Systems as Action-Minimizing Paths in the Wasserstein Space

Archive for Rational Mechanics and Analysis ◽

10.1007/s00205-008-0148-y ◽

2008 ◽

Vol 192 (3) ◽

pp. 419-452 ◽

Author(s):

W. Gangbo ◽

T. Nguyen ◽

A. Tudorascu

Keyword(s):

Wasserstein Space

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Busemann functions on the Wasserstein space

Calculus of Variations and Partial Differential Equations ◽

10.1007/s00526-021-01937-3 ◽

2021 ◽

Vol 60 (3) ◽

Author(s):

Guomin Zhu ◽

Wen-Long Li ◽

Xiaojun Cui

Keyword(s):

Busemann Functions ◽

Wasserstein Space

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Finsler structure in the p-Wasserstein space and gradient flows

Comptes Rendus Mathematique ◽

10.1016/j.crma.2011.11.014 ◽

2012 ◽

Vol 350 (1-2) ◽

pp. 35-40 ◽

Author(s):

Martial Agueh

Keyword(s):

Gradient Flows ◽

Finsler Structure ◽

Wasserstein Space

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The Parisi formula is a Hamilton-Jacobi equation in Wasserstein space

Canadian Journal of Mathematics ◽

10.4153/s0008414x21000031 ◽

2021 ◽

pp. 1-23

Author(s):

Jean-Christophe Mourrat

Keyword(s):

Jacobi Equation ◽

Parisi Formula ◽

Wasserstein Space ◽

Hamilton Jacobi Equation

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On the Lagrangian description of absolutely continuous curves in the Wasserstein space on the line; well-posedness for the Continuity Equation

Indiana University Mathematics Journal ◽

10.1512/iumj.2015.64.5727 ◽

2015 ◽

Vol 64 (6) ◽

pp. 1835-1877

Author(s):

Adrian Tudorascu ◽

Mohamed Amsaad

Keyword(s):

Continuity Equation ◽

Lagrangian Description ◽

Well Posedness ◽

Absolutely Continuous ◽

Wasserstein Space ◽

Continuous Curves

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Second-Order Models for Optimal Transport and Cubic Splines on the Wasserstein Space

Foundations of Computational Mathematics ◽

10.1007/s10208-019-09425-z ◽

2019 ◽

Vol 19 (5) ◽

pp. 1113-1143 ◽

Author(s):

Jean-David Benamou ◽

Thomas O. Gallouët ◽

François-Xavier Vialard

Keyword(s):

Optimal Transport ◽

Cubic Splines ◽

Second Order ◽

Wasserstein Space

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Wasserstein space as state space of quantum mechanics and optimal transport

Journal of Physics Conference Series ◽

10.1088/1742-6596/1170/1/012006 ◽

2019 ◽

Vol 1170 ◽

pp. 012006

Author(s):

M F Rosyid ◽

K Wahyuningsih

Keyword(s):

Quantum Mechanics ◽

State Space ◽

Optimal Transport ◽

Wasserstein Space

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Optimal control of multiagent systems in the Wasserstein space

Calculus of Variations and Partial Differential Equations ◽

10.1007/s00526-020-1718-6 ◽

2020 ◽

Vol 59 (2) ◽

Author(s):

Chloé Jimenez ◽

Antonio Marigonda ◽

Marc Quincampoix

Keyword(s):

Optimal Control ◽

Multiagent Systems ◽

Wasserstein Space

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q-Heat flow and the gradient flow of the Renyi entropy in the p-Wasserstein space

Journal of Functional Analysis ◽

10.1016/j.jfa.2016.06.016 ◽

2016 ◽

Vol 271 (8) ◽

pp. 2045-2089 ◽

Author(s):

Martin Kell

Keyword(s):

Heat Flow ◽

Gradient Flow ◽

Renyi Entropy ◽

Rényi Entropy ◽

Wasserstein Space

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The heat equation on manifolds as a gradient flow in the Wasserstein space

Annales de l Institut Henri Poincaré Probabilités et Statistiques ◽

10.1214/08-aihp306 ◽

2010 ◽

Vol 46 (1) ◽

pp. 1-23 ◽

Author(s):

Matthias Erbar

Keyword(s):

Heat Equation ◽

Gradient Flow ◽

Wasserstein Space

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Wasserstein space over the Wiener space

Probability Theory and Related Fields ◽

10.1007/s00440-009-0199-5 ◽

2009 ◽

Vol 146 (3-4) ◽

pp. 535-565 ◽

Author(s):

Shizan Fang ◽

Jinghai Shao ◽

Karl-Theodor Sturm

Keyword(s):

Wiener Space ◽

Wasserstein Space

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