$\Gamma$-convergence for a class of action functionals induced by gradients of convex functions

Autor: Yann Brenier, Luigi Ambrosio, Aymeric Baradat

Publikováno v: Rendiconti Lincei - Matematica e Applicazioni. 32:97-108

Given a real function $f$, the rate function for the large deviations of the diffusion process of drift $\nabla f$ given by the Freidlin-Wentzell theorem coincides with the time integral of the energy dissipation for the gradient flow associated with

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9b302ec88e47dff095b3f3c672994dab
https://doi.org/10.4171/rlm/928

ON OPTIMAL TRANSPORT OF MATRIX-VALUED MEASURES

Autor: Yann Brenier, Dmitry Vorotnikov

We suggest a new way of defining optimal transport of positive-semidefinite matrix-valued measures. It is inspired by a recent rendering of the incompressible Euler equations and related conservative systems as concave maximization problems. The main

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::79ffbfbf3c3ea3faab94409d51a33cc0
https://hal.archives-ouvertes.fr/hal-02389318

Optimal transportation of particles, fluids and currents

Autor: Yann Brenier

Publikováno v: Variational Methods for Evolving Objects, L. Ambrosio, Y. Giga, P. Rybka and Y. Tonegawa, eds. (Tokyo: Mathematical Society of Japan, 2015)

In these lectures, we review a series of optimal transport (OT) problems of growing complexity. Surprisingly enough, in this seemingly narrow framework, we will encounter nonlinear PDEs of very different type, such as the Monge–Ampère équation, t

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https://doi.org/10.2969/aspm/06710059

An integrable example of gradient flow based on optimal transport of differential forms

Autor: Yann Brenier, Xianglong Duan

Publikováno v: Calculus of Variations and Partial Differential Equations. 57

Optimal transport theory has been a powerful tool for the analysis of parabolic equations viewed as gradient flows of volume forms according to suitable transportation metrics. In this paper, we present an example of gradient flows for closed (d-1)-f

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https://doi.org/10.1007/s00526-018-1370-6

Some Concepts of Generalized and Approximate Solutions in Ideal Incompressible Fluid Mechanics Related to the Least Action Principle

Autor: Yann Brenier

Publikováno v: New Trends and Results in Mathematical Description of Fluid Flows ISBN: 9783319943428

Various concepts of generalized and approximate solutions related to the mathematical theory of ideal incompressible fluids are discussed in relation with variational and stochastic approaches, in close connection with the least action principle.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::9d9dbc30c1421367c020e5d9d754b322
https://doi.org/10.1007/978-3-319-94343-5_2