Optimal transportation and action. Minimizing measures

of probability measures on a manifold endowed with a notion of distance derived from the optimal ... action minimizing curve or an optimal trajectory from x to y. Optimal transportation and action-minimizing measures. par Alessio Figalli. Thèse de doctorat en Mathématiques. Sous la direction de Cédric Villani. Soutenue ...

underline the formal similarity between the problem of action minimizing curves and some dynamic optimal transportation problem as discussed in [7] and other papers. We obtain general existence results for these questions. In order to study the minimizing measures in a general framework, we need to pursue the study of transport measures. We show that the transportation can be interpolated by a Lipschitz lamination. We describe several direct variational problems the minimizers of which are these Lipschitz laminations. We prove the existence of an optimal transport map when the transported measure is absolutely continuous. We explain the relations with Mather’s minimal measures.

0)♯m0 = m0 and is minimizing the action. A1. 0(m0) = ∫. TM×[0,1]. L(ψt. 0(x, v),t) dm0dt. The major discovery of [28] is that Mather measures are supported on ...

Optimal transportation and action. Minimizing measures è un libro di Figalli Alessio pubblicato da Scuola Normale Superiore (EN) nella collana Tesi - ISBN: 9788876423307

Optimal Transportation and Action-Minimizing Measures. Front Cover. Alessio Figalli. Scuola Normale Superiore, Jul 17, 2008 - Mathematics - 254 pages. of probability measures on a manifold endowed with a notion of distance derived from the optimal ... action minimizing curve or an optimal trajectory from x to y.