Advances in Differential Equations

Duality theory and optimal transport for sand piles growing in a silos

Luigi De Pascale and Chloé Jimenez

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We prove existence and uniqueness of solutions for a system of PDEs which describes the growth of a sandpile in a silos with flat bottom under the action of a vertical, measure source. The tools we use are a discrete approximation of the source and the duality theory for optimal transport (or Monge-Kantorovich) problems.

Article information

Adv. Differential Equations, Volume 20, Number 9/10 (2015), 859-886.

First available in Project Euclid: 23 June 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 49Q20: Variational problems in a geometric measure-theoretic setting 35K20: Initial-boundary value problems for second-order parabolic equations 35K55: Nonlinear parabolic equations 47J20: Variational and other types of inequalities involving nonlinear operators (general) [See also 49J40] 49K30: Optimal solutions belonging to restricted classes 35B99: None of the above, but in this section


De Pascale, Luigi; Jimenez, Chloé. Duality theory and optimal transport for sand piles growing in a silos. Adv. Differential Equations 20 (2015), no. 9/10, 859--886.

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