28/05/2024, 10:00 at Aula di Consiglio - Dipartimento di Matematica "G. Castelnuovo"
Ore 10:00 Saluti della Direttrice del Dipartimento di Matematica "G. Castelnuovo"
Ore 10:10 David Arcoya (Univ. di Granada)
Back to Landesman-lazer conditions and quasilinear elliptic equations
Ore 10:45 Marco Picerni (Sapienza)
Existence and regularity of solutions of a parabolic-elliptic nonlinear system
Abstract: We prove the existence of a solution of a parabolic-elliptic nonlinear system related to the Keller-Segel model for chemotaxis, which is the pairing of a Fokker-Planck type equation and a linear elliptic equation.
We prove that such a solution obeys an equivalent of Stampacchia's regularity results for linear parabolic equations. This regularizing effect can be entirely attributed to the interplay between the two equations of the system, since it was shown that, without sufficient regularity of the drift term, it is only possible to find highly singular entropy solutions of the Fokker-Planck equation.
Ore 11:00 Alessio Porretta (Univ. Tor Vergata)
Diffusive effects in optimal transport with congestion
Abstract. We discuss optimal transport problems with density dependent terms, penalizing congestion effects. Those terms enhance some form of dissipation compared to the classical Monge-Kantorovich transport. In particular we discuss properties like L^1-L^\infty regularization, displacement convexity, self-similar solutions and free boundary regularity when the support propagates with finite speed.
Ore 11:35 Lucio Boccardo
Some remarks on a paper by Fortunato-Pisani concerning Born–Infeld-Orsina type equations for electrostatic fields.
Ore 11:55 Saluti Finali