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Article Dans Une Revue ESAIM: Control, Optimisation and Calculus of Variations Année : 2019

Minimizing acceleration on the group of diffeomorphisms and its relaxation

Résumé

We study a second-order variational problem on the group of diffeomorphisms of the interval [0, 1] endowed with a right-invariant Sobolev metric of order 2, which consists in the minimization of the acceleration. We compute the relaxation of the problem which involves the so-called Fisher–Rao functional, a convex functional on the space of measures. This relaxation enables the derivation of several optimality conditions and, in particular, a sufficient condition which guarantees that a given path of the initial problem is also a minimizer of the relaxed one. Based on these sufficient conditions, the main result is that, when the value of the (minimized) functional is small enough, the minimizers are classical, that is the defect measure vanishes.

Dates et versions

hal-04497577 , version 1 (10-03-2024)

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Rabah Tahraoui, François-Xavier Vialard. Minimizing acceleration on the group of diffeomorphisms and its relaxation. ESAIM: Control, Optimisation and Calculus of Variations, 2019, 25, pp.70. ⟨10.1051/cocv/2018068⟩. ⟨hal-04497577⟩
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