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On the minimizing movement with the 1-Wasserstein distance

Agueh, Martial; Carlier, Guillaume; Igbida, Noureddine (2018), On the minimizing movement with the 1-Wasserstein distance, ESAIM: Control, Optimisation and Calculus of Variations, 24, 4 (October–December 2018 ), p. 1415 - 1427. 10.1051/cocv/2017055

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Article accepté pour publication ou publié
External document link
https://hal.archives-ouvertes.fr/hal-01467979
Date
2018
Journal name
ESAIM: Control, Optimisation and Calculus of Variations
Volume
24
Number
4 (October–December 2018 )
Pages
1415 - 1427
Publication identifier
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Author(s)
Agueh, Martial
Dept. of Mathematics, University of Victoria
Carlier, Guillaume
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Igbida, Noureddine
Abstract (EN)
We consider a class of doubly nonlinear constrained evolution equations which may be viewed as a nonlinear extension of the growing sandpile model of [15]. We prove existence of weak solutions for quite irregular sources by a semi-implicit scheme in the spirit of the seminal works of [13] and [14] but with the 1-Wasserstein distance instead of the quadratic one. We also prove an L 1-contraction result when the source is L 1 and deduce uniqueness and stability in this case.
Subjects / Keywords
L 1 -contraction; 1-Wasserstein distance; minimizing movement; growingsandpiles