Comptes Rendus
no. 7
Partial differential equations/Calculus of variations
Minimizing movements along a sequence of functionals and curves of maximal slope
[Mouvements minimisants le long d'une séquence de fonctionnelles et courbes de pente maximale]

Présenté par : Haïm Brézis

Andrea Braides1 ; Maria Colombo2 ; Massimo Gobbino3 ; Margherita Solci4
1 Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma, Italy
2 ETH Institute for Theoretical Studies, Clausiusstrasse 47, CH-8092 Zürich, Switzerland
3 Dipartimento di Matematica, Via Filippo Buonarroti 1c, 56127 Pisa, Italy
4 DADU, Università di Sassari, Piazza Duomo 6, 07041 Alghero (SS), Italy
Comptes Rendus. Mathématique, Volume 354 (2016) no. 7, pp. 685-689.

Nous montrons qu'une condition générale présentée par Colombo et Gobbino pour étudier les limites des courbes de pente maximale permet également de caractériser les mouvements minimisants le long d'une séquence de fonctionelles comme des courbes de pente maximale de la fonctionnelle limite.

We prove that a general condition introduced by Colombo and Gobbino to study limits of curves of maximal slope allows us to characterize also minimizing movements along a sequence of functionals as curves of maximal slope of a limit functional.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2016.04.011
Andrea Braides 1 ; Maria Colombo 2 ; Massimo Gobbino 3 ; Margherita Solci 4

1 Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma, Italy
2 ETH Institute for Theoretical Studies, Clausiusstrasse 47, CH-8092 Zürich, Switzerland
3 Dipartimento di Matematica, Via Filippo Buonarroti 1c, 56127 Pisa, Italy
4 DADU, Università di Sassari, Piazza Duomo 6, 07041 Alghero (SS), Italy 
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     title = {Minimizing movements along a sequence of functionals and curves of maximal slope},
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Andrea Braides; Maria Colombo; Massimo Gobbino; Margherita Solci. Minimizing movements along a sequence of functionals and curves of maximal slope. Comptes Rendus. Mathématique, Volume 354 (2016) no. 7, pp. 685-689. doi : 10.1016/j.crma.2016.04.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.04.011/

[1] F. Almgren; J.E. Taylor Flat flow is motion by crystalline curvature for curves with crystalline energies, J. Differ. Geom., Volume 42 (1995), pp. 1-22

[2] L. Ambrosio; N. Gigli A user's guide to optimal transport (B. Piccoli; M. Rascle, eds.), Modelling and Optimisation of Flows on Networks, Lecture Notes in Mathematics, Springer, Berlin, 2013, pp. 1-155

[3] L. Ambrosio; N. Gigli; G. Savaré Gradient Flows in Metric Spaces and in the Space of Probability Measures, Lectures in Mathematics ETH, Zürich, Birkhhäuser, Basel, Switzerland, 2008

[4] A. Braides Local Minimization, Variational Evolution and Γ-convergence, Springer Verlag, Berlin, 2014

[5] A. Braides; A. Defranceschi; E. Vitali Variational evolution of one-dimensional Lennard–Jones systems, Netw. Heterog. Media, Volume 9 (2014), pp. 217-238

[6] A. Braides; M.S. Gelli; M. Novaga Motion and pinning of discrete interfaces, Arch. Ration. Mech. Anal., Volume 95 (2010), pp. 469-498

[7] M. Colombo; M. Gobbino Passing to the limit in maximal slope curves: from a regularized Perona–Malik equation to the total variation flow, Math. Models Methods Appl. Sci., Volume 22 (2012), p. 1250017

[8] E. Sandier; S. Serfaty Gamma-convergence of gradient flows and application to Ginzburg–Landau, Commun. Pure Appl. Math., Volume 57 (2004), pp. 1627-1672

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