Outputs (3)

A gradient flow perspective on the quantization problem (2018)
Presentation / Conference Contribution
Iacobelli, M., Cardaliaguet, P., Porretta, A., & Salvarani, F. (2018, December). A gradient flow perspective on the quantization problem. Presented at PDE Models for Multi-Agent Phenomena, Rome, Italy

In this paper we review recent results by the author on the problem of quantization of measures. More precisely, we propose a dynamical approach, and we investigate it in dimensions 1 and 2. Moreover, we discuss a recent general result on the static... Read More about A gradient flow perspective on the quantization problem.

Weighted ultrafast diffusion equations: from well-posedness to long-time behaviour (2018)
Journal Article
Iacobelli, M., Patacchini, F., & Santambrogio, F. (2019). Weighted ultrafast diffusion equations: from well-posedness to long-time behaviour. Archive for Rational Mechanics and Analysis, 232(3), 1165-1206. https://doi.org/10.1007/s00205-018-01341-w

In this paper we devote our attention to a class of weighted ultrafast diffusion equations arising from the problem of quantisation for probability measures. These equations have a natural gradient flow structure in the space of probability measures... Read More about Weighted ultrafast diffusion equations: from well-posedness to long-time behaviour.

A mean field approach to the quasineutral limit for the Vlasov-Poisson equation (2018)
Journal Article
Griffin-Pickering, M., & Iacobelli, M. (2018). A mean field approach to the quasineutral limit for the Vlasov-Poisson equation. SIAM Journal on Mathematical Analysis, 50(5), 5502-5536. https://doi.org/10.1137/17m1156277

This paper concerns the derivation of the Kinetic Isothermal Euler system in dimension d≥1 from an N-particle system of extended charges with Coulomb interaction. This requires a combined mean field and quasineutral limit for a regularized N-particle... Read More about A mean field approach to the quasineutral limit for the Vlasov-Poisson equation.