16 citations · 48 across the 14 of their papers we have counts for
15 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…
De Giorgi-Nash-Moser theory for kinetic equations with nonlocal diffusions
Francesca Anceschi, Giampiero Palatucci, Mirco Piccinini
We extend the De Giorgi--Nash--Moser theory to nonlocal hypoelliptic equations arising in kinetic theory as linearized models for the non-cutoff Boltzmann equation. Assuming that t…
Poincaré inequality and quantitative De Giorgi method for hypoelliptic operators
Francesca Anceschi, Helge Dietert, Jessica Guerand +3
We propose a systematic approach based on trajectories to prove a Poincaré inequality for weak non-negative sub-solutions to hypoelliptic equations with an arbitrary number of Hörm…
New perspectives on recent trends for Kolmogorov operators
Francesca Anceschi, Mirco Piccinini, Annalaura Rebucci
After carrying out an overview on the non Euclidean geometrical setting suitable for the study of Kolmogorov operators with rough coefficients, we list some properties of the funct…
On the obstacle problem associated to the Kolmogorov-Fokker-Planck operator with rough coefficients
Francesca Anceschi, Annalaura Rebucci
This work is devoted to the study of the obstacle problem associated to the Kolmogorov-Fokker-Planck operator with rough coefficients through a variational approach. In particular,…
Boundedness estimates for nonlinear nonlocal kinetic Kolmogorov-Fokker-Planck equations
Francesca Anceschi, Mirco Piccinini
We investigate local regularity properties of weak solutions to a broad class of nonlinear nonlocal kinetic Kolmogorov-Fokker-Planck equations. In particular, we focus on proving a…
Harnack inequality and asymptotic lower bounds for the relativistic Fokker-Planck operator
Francesca Anceschi, Sergio Polidoro, Annalaura Rebucci
We consider a class of second order degenerate kinetic operators in the framework of special relativity. We first describe as an Hörmander operator whic…
Spatial regularity for a class of degenerate Kolmogorov equations
Francesca Anceschi
We establish spatial a priori estimates for the solution u to a class of dilation invariant Kolmogorov equation, where u is assumed to only have a certain amount of regularity in t…
A note on the weak regularity theory for degenerate Kolmogorov equations
Francesca Anceschi, Annalaura Rebucci
The aim of this work is to prove a Harnack inequality and the Hölder continuity for weak solutions to the Kolmogorov equation with measurable coefficients, inte…
On a spatially inhomogeneous nonlinear Fokker-Planck equation: Cauchy problem and diffusion asymptotics
Francesca Anceschi, Yuzhe Zhu
We investigate the Cauchy problem and the diffusion asymptotics for a spatially inhomogeneous kinetic model associated to a nonlinear Fokker-Planck operator. We derive the global w…
Existence of a Fundamental Solution of Partial Differential Equations associated to Asian Options
Francesca Anceschi, Silvia Muzzioli, Sergio Polidoro
We prove the existence and uniqueness of the fundamental solution for Kolmogorov operators associated to some stochastic processes, that arise in the Black & Scholes setting for th…
A survey on the classical theory for Kolmogorov equation
Francesca Anceschi, Sergio Polidoro
We present a survey on the regularity theory for classic solutions to subelliptic degenerate Kolmogorov equations. In the last part of this note we present a detailed proof of a Ha…
Moser's estimates for degenerate Kolmogorov equations with non-negative divergence lower order coefficients
Francesca Anceschi, Sergio Polidoro, Maria Alessandra Ragusa
We prove the local boundedness of the solutions to degenerate second order partial differential equations of Kolmogorov type with measurable coefficients in divergence form, under…
A geometric statement of the Harnack inequality for a degenerate Kolmogorov equation with rough coefficients
Francesca Anceschi, Michela Eleuteri, Sergio Polidoro
We consider weak solutions of degenerate second order partial differential equations of Kolmogorov-Fokker-Planck type with measurable coefficients in divergence form. We give a geo…