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Article Dans Une Revue ESAIM: Control, Optimisation and Calculus of Variations Année : 2018

On the minimizing movement with the 1-Wasserstein distance

Résumé

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.
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hal-01467979 , version 1 (15-02-2017)

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  • HAL Id : hal-01467979 , version 1

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Martial Agueh, Guillaume Carlier, Noureddine Igbida. On the minimizing movement with the 1-Wasserstein distance. ESAIM: Control, Optimisation and Calculus of Variations, 2018. ⟨hal-01467979⟩
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