Displaying similar documents to “Gradient flows with metric and differentiable structures, and applications to the Wasserstein space”

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

Matthias Erbar (2010)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

We study the gradient flow for the relative entropy functional on probability measures over a riemannian manifold. To this aim we present a notion of a riemannian structure on the Wasserstein space. If the Ricci curvature is bounded below we establish existence and contractivity of the gradient flow using a discrete approximation scheme. Furthermore we show that its trajectories coincide with solutions to the heat equation.

Gradient flows in Wasserstein spaces and applications to crowd movement

Filippo Santambrogio (2010-2011)

Séminaire Équations aux dérivées partielles

Similarity:

Starting from a motivation in the modeling of crowd movement, the paper presents the topics of gradient flows, first in ℝ n , then in metric spaces, and finally in the space of probability measures endowed with the Wasserstein distance (induced by the quadratic transport cost). Differently from the usual theory by Jordan-Kinderlehrer-Otto and Ambrosio-Gigli-Savaré, we propose an approach where the optimality conditions for the minimizers of the optimization problems that one solves at every...

Gradient flows in Wasserstein spaces and applications to crowd movement

Filippo Santambrogio (2009-2010)

Séminaire Équations aux dérivées partielles

Similarity:

Starting from a motivation in the modeling of crowd movement, the paper presents the topics of gradient flows, first in ℝ n , then in metric spaces, and finally in the space of probability measures endowed with the Wasserstein distance (induced by the quadratic transport cost). Differently from the usual theory by Jordan-Kinderlehrer-Otto and Ambrosio-Gigli-Savaré, we propose an approach where the optimality conditions for the minimizers of the optimization problems that one solves at every...

Some problems of parabolic type with discontinuous nonlinearities on convex constraints

Marlène Frigon, Antonio Marino, Claudio Saccon (1990)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

We study semilinear equations and inequalities of parabolic type with discontinuous nonlinearities, possibly subjected to convex or even nonconvex constraint conditions. To prove some existence theorems we regard the solutions as «curves of maximal relaxed slope» for a suitable functional on the given constraint.

Gehring's lemma for metrics and higher integrability of the gradient for minimizers of noncoercive variational functionals

Bruno Franchi, Francesco Serra Cassano (1996)

Studia Mathematica

Similarity:

We prove a higher integrability result - similar to Gehring's lemma - for the metric space associated with a family of Lipschitz continuous vector fields by means of sub-unit curves. Applications are given to show the higher integrability of the gradient of minimizers of some noncoercive variational functionals.