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
TypeArticle accepté pour publication ou publié
External document linkhttps://hal.archives-ouvertes.fr/hal-01467979
Journal nameESAIM: Control, Optimisation and Calculus of Variations
Number4 (October–December 2018 )
MetadataShow full item record
Dept. of Mathematics, University of Victoria
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
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 . We prove existence of weak solutions for quite irregular sources by a semi-implicit scheme in the spirit of the seminal works of  and  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 / KeywordsL 1 -contraction; 1-Wasserstein distance; minimizing movement; growingsandpiles
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