On the minimizing movement with the 1-Wasserstein distance

Abstract : 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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https://hal.archives-ouvertes.fr/hal-01467979
Contributor : Guillaume Carlier <>
Submitted on : Wednesday, February 15, 2017 - 12:33:18 AM
Last modification on : Tuesday, May 28, 2019 - 4:40:41 PM
Long-term archiving on : Tuesday, May 16, 2017 - 12:20:58 PM

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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. 2017. ⟨hal-01467979⟩

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