70 citations · 169 across the 27 of their papers we have counts for
36 papers
Long-time contractivity estimates for kinetic Kolmogorov-Fokker-Planck equations
Nicolò Forcillo, Alessio Porretta
We prove long-time contractivity estimates and exponential rates of convergence to equilibrium for solutions of hypoelliptic diffusion equations, which include the well-known Kolmo…
Classification of solutions of an elliptic Hamilton-Jacobi equation
Alessio Porretta, Philippe Souplet
We show that any classical solution of the diffusive Hamilton-Jacobi (DHJ) equation in a half-space with zero boundary conditions for is necessarily…
Diffuse measures and nonlinear parabolic equations
Francesco Petitta, Augusto C. Ponce, Alessio Porretta
Given a parabolic cylinder , where is a bounded domain, we prove new properties of solutions of \[ u_t-Δ_p u = μ\quad \text{in } \] wi…
Transporting a Dirac mass in a mean field planning problem
Pierre Cardaliaguet, Sebastian Munoz, Alessio Porretta
We study a mean field planning problem in which the initial density is a Dirac mass. We show that there exists a unique solution which converges to a self-similar profile as time t…
Long time behaviour of Mean Field Games with fractional diffusion
Olav Ersland, Espen Robstad Jakobsen, Alessio Porretta
In this paper we study the long time behaviour of mean field games systems with fractional diffusion, modeling the case that the individual dynamics of the players is driven by ind…
Entropy-minimizing dynamical transport on Riemannian manifolds
Gabriele Bocchi, Alessio Porretta
Given a smooth Riemannian manifold , compact and without boundary, we analyze the dynamical optimal mass transport problem where the cost is given by the sum of the kinetic…