Displaying similar documents to “Wasserstein gradient flows from large deviations of many-particle limits”

Gradient flows in Wasserstein spaces and applications to crowd movement

Filippo Santambrogio (2010-2011)

Séminaire Équations aux dérivées partielles

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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...

Anisotropic geometric functionals and gradient flows

Giovanni Bellettini, Luca Mugnai (2009)

Banach Center Publications

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We survey some recent results on the gradient flow of an anisotropic surface energy, the integrand of which is one-homogeneous in the normal vector. We discuss the reasons for assuming convexity of the anisotropy, and we review some known results in the smooth, mixed and crystalline case. In particular, we recall the notion of calibrability and the related facet-breaking phenomenon. Minimal barriers as weak solutions to the gradient flow in case of nonsmooth anisotropies are proposed....

Non-local approximation of functionals: variational and evolution problems

Massimo Gobbino (2000)

Bollettino dell'Unione Matematica Italiana

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Questa nota tratta dell'approssimazione di funzionali, usati in problemi con discontinuità libere, mediante famiglie di funzionali non locali in cui il gradiente è sostituito dal rapporto incrementale. Vengono inoltre presentate alcune applicazioni di questa teoria a problemi variazionali e di evoluzione.