7 papers
Well-posedness of Kolmogorov-Fokker-Planck equations with unbounded drift
Francesca Anceschi, Giacomo Ascione, Daniele Castorina +1
We consider Kolmogorov-Fokker-Planck equations with unbounded drift terms which are only measurable in time and locally Hölder continuous in space. In particular, we extend the par…
Mean field sparse optimal control of systems with additive white noise
Giacomo Ascione, Daniele Castorina, Francesco Solombrino
We analyze the problem of controlling a multi-agent system with additive white noise through parsimonious interventions on a selected subset of the agents (leaders). For such a con…
Semilinear Li & Yau inequalities
Daniele Castorina, Giovanni Catino, Carlo Mantegazza
We derive an adaptation of Li & Yau estimates for positive solutions of semilinear heat equations on Riemannian manifolds with nonnegative Ricci tensor. We then apply these estimat…
A matrix Harnack inequality for semilinear heat equations
Giacomo Ascione, Daniele Castorina, Giovanni Catino +1
We derive a matrix version of Li \& Yau--type estimates for positive solutions of semilinear heat equations on Riemannian manifolds with nonnegative sectional curvatures and parall…
A Triviality Result for Semilinear Parabolic Equations
Giovanni Catino, Daniele Castorina, Carlo Mantegazza
We show a triviality result for "pointwise" monotone in time, bounded "eternal" solutions of the semilinear heat equation \begin{equation*} u_{t}=Δu + |u|^{p} \end{equation*} on co…
A Liouville theorem for superlinear heat equations on Riemannian manifolds
Daniele Castorina, Carlo Mantegazza, Berardino Sciunzi
We study the triviality of the solutions of weighted superlinear heat equations on Riemannian manifolds with nonnegative Ricci tensor. We prove a Liouville--type theorem for soluti…