55 citations · 104 across the 14 of their papers we have counts for
17 papers
Optimal control problems driven by nonlinear degenerate Fokker-Planck equations
Francesca Anceschi, Giacomo Ascione, Daniele Castorina +1
The well-posedness of a class of optimal control problems is analysed, where the state equation couples a nonlinear degenerate Fokker-Planck equation with a system of Ordinary Diff…
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…
Hopf Lemma and regularity results for quasilinear anisotropic elliptic equations
Daniele Castorina, Giuseppe Riey, Berardino Sciunzi
We consider a class of quasi-linear anisotropic elliptic equations, possibly degenerate or singular, which are of interest in several applications such as computer vision and conti…
Ancient solutions of superlinear heat equations on Riemannian manifolds
Daniele Castorina, Carlo Mantegazza
We study some qualitative properties of ancient solutions of superlinear heat equations on a Riemannian manifold, with particular interest in positivity and constancy in space.
On a singular Liouville-type equation and the Alexandrov isoperimetric inequality
Daniele Bartolucci, Daniele Castorina
We obtain a generalized version of an inequality, first derived by C. Bandle in the analytic setting, for weak subsolutions of a singular Liouville-type equation. As an application…
On a parabolic Hamilton-Jacobi-Bellman equation degenerating at the boundary
Daniele Castorina, Annalisa Cesaroni, Luca Rossi
We derive the long time asymptotic of solutions to an evolutive Hamilton-Jacobi-Bellman equation in a bounded smooth domain, in connection with ergodic problems recently studied in…
A global existence result for a Keller-Segel type system with supercritical initial data
Daniele Bartolucci, Daniele Castorina
We consider a parabolic-elliptic Keller-Segel type system, which is related to a simplified model of chemotaxis. Concerning the maximal range of existence of solutions, there are e…
Self gravitating cosmic strings and the Alexandrov's inequality for Liouville-type equations
Daniele Bartolucci, Daniele Castorina
Motivated by the study of self gravitating cosmic strings, we pursue the well known method by C. Bandle to obtain a weak version of the classical Alexandrov's isoperimetric inequal…
Regularity of the extremal solution for singular p-Laplace equations
Daniele Castorina
We study the regularity of the extremal solution to the singular reaction-diffusion problem in , on , where , , $Ω\s…
Ground States for Diffusion Dominated Free Energies with Logarithmic Interaction
José Antonio Carrillo, Daniele Castorina, Bruno Volzone
Replacing linear diffusion by a degenerate diffusion of porous medium type is known to regularize the classical two-dimensional parabolic-elliptic Keller-Segel model. The implicati…
Regularity of stable solutions to semilinear elliptic equations on Riemannian models
Daniele Castorina, Manel Sanchon
We consider the reaction-diffusion problem in with zero Dirichlet boundary condition, posed in a geodesic ball with radius of a…
Regularity of stable solutions of -Laplace equations through geometric Sobolev type inequalities
Daniele Castorina, Manel Sanchon
In this paper we prove a Sobolev and a Morrey type inequality involving the mean curvature and the tangential gradient with respect to the level sets of the function that appears i…