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math.AP2025
A PDE perspective on the flat chain conjecture
Andrea Marchese
This survey summarizes recent progress on the flat chain conjecture, which asserts the equivalence between metric currents and flat chains with finite mass in the Euclidean space.…
math.AP2025
Variational models of robust optimal transport
Luigi De Masi, Andrea Marchese, Annalisa Massaccesi
This paper introduces two variational formulations for a model of robust optimal transport, that is, the problem of designing optimal transport networks that are resilient to poten…
math.AP2024
A refined Lusin type theorem for gradients
Luigi De Masi, Andrea Marchese
We prove a refined version of the celebrated Lusin type theorem for gradients by Alberti, stating that any Borel vector field coincides with the gradient of a function $g…