Outputs (4)

First Order Mean Field Games with Density Constraints: Pressure Equals Price (2016)
Journal Article
Cardaliaguet, P., Mészáros, A. R., & Santambrogio, F. (2016). First Order Mean Field Games with Density Constraints: Pressure Equals Price. SIAM Journal on Control and Optimization, 54(5), 2672-2709. https://doi.org/10.1137/15m1029849

In this paper we study mean field game systems under density constraints as optimality conditions of two optimization problems in duality. A weak solution of the system contains an extra term, an additional price imposed on the saturated zones. We sh... Read More about First Order Mean Field Games with Density Constraints: Pressure Equals Price.

Uniqueness issues for evolution equations with density constraints (2016)
Journal Article
Di Marino, S., & Mészáros, A. R. (2016). Uniqueness issues for evolution equations with density constraints. Mathematical Models and Methods in Applied Sciences, 26(09), 1761-1783. https://doi.org/10.1142/s0218202516500445

In this paper, we present some basic uniqueness results for evolution equations under density constraints. First, we develop a rigorous proof of a well-known result (among specialists) in the case where the spontaneous velocity field satisfies a mono... Read More about Uniqueness issues for evolution equations with density constraints.

Advection-diffusion equations with density constraints (2016)
Journal Article
Mészáros, A. R., & Santambrogio, F. (2016). Advection-diffusion equations with density constraints. Analysis & PDE, 9(3), 615-644. https://doi.org/10.2140/apde.2016.9.615

In the spirit of the macroscopic crowd motion models with hard congestion (i.e., a strong density constraint ρ≤1) introduced by Maury et al. some years ago, we analyze a variant of the same models where diffusion of the agents is also taken into acco... Read More about Advection-diffusion equations with density constraints.

BV Estimates in Optimal Transportation and Applications (2016)
Journal Article
De Philippis, G., Mészáros, A. R., Santambrogio, F., & Velichkov, B. (2016). BV Estimates in Optimal Transportation and Applications. Archive for Rational Mechanics and Analysis, 219(2), 829-860. https://doi.org/10.1007/s00205-015-0909-3

In this paper we study the BV regularity for solutions of certain variational problems in Optimal Transportation. We prove that the Wasserstein projection of a measure with BV density on the set of measures with density bounded by a given BV function... Read More about BV Estimates in Optimal Transportation and Applications.