A survey on the classical theory for Kolmogorov equation
F Anceschi, S Polidoro - arXiv preprint arXiv:1907.05155, 2019 - arxiv.org
arXiv:1907.05155v2 [math.AP] 30 Jul 2019 Page 1 arXiv:1907.05155v2 [math.AP] 30 Jul 2019
A survey on the classical theory for Kolmogorov equation Francesca Anceschi ∗ Sergio …
A survey on the classical theory for Kolmogorov equation Francesca Anceschi ∗ Sergio …
Optimal regularity for degenerate Kolmogorov equations in non-divergence form with rough-in-time coefficients
S Pagliarani, G Lucertini, A Pascucci - Journal of Evolution Equations, 2023 - Springer
We consider a class of degenerate equations in non-divergence form satisfying a parabolic
Hörmander condition, with coefficients that are measurable in time and Hölder continuous in …
Hörmander condition, with coefficients that are measurable in time and Hölder continuous in …
On stochastic Langevin and Fokker-Planck equations: the two-dimensional case
A Pascucci, A Pesce - Journal of Differential Equations, 2022 - Elsevier
We prove existence, regularity in Hölder classes and estimates from above and below of the
fundamental solution of the stochastic Langevin equation that is a degenerate SPDE …
fundamental solution of the stochastic Langevin equation that is a degenerate SPDE …
On the fundamental solution for degenerate Kolmogorov equations with rough coefficients
F Anceschi, A Rebucci - Journal of elliptic and parabolic equations, 2023 - Springer
The aim of this work is to prove the existence of a fundamental solution associated to the
Kolmogorov equation L u= f in the dilation invariant case, with bounded measurable first …
Kolmogorov equation L u= f in the dilation invariant case, with bounded measurable first …
[HTML][HTML] Sobolev embeddings for kinetic Fokker-Planck equations
A Pascucci, A Pesce - Journal of Functional Analysis, 2024 - Elsevier
Abstract We introduce intrinsic Sobolev-Slobodeckij spaces for a class of ultra-parabolic
Kolmogorov type operators satisfying the weak Hörmander condition. We prove continuous …
Kolmogorov type operators satisfying the weak Hörmander condition. We prove continuous …
Optimal Schauder estimates for kinetic Kolmogorov equations with time measurable coefficients
G Lucertini, S Pagliarani, A Pascucci - arXiv preprint arXiv:2304.13392, 2023 - arxiv.org
We prove global Schauder estimates for kinetic Kolmogorov equations with coefficients that
are H\" older continuous in the spatial variables but only measurable in time. Compared to …
are H\" older continuous in the spatial variables but only measurable in time. Compared to …
Degenerate McKean-Vlasov equations with drift in anisotropic negative Besov spaces
E Issoglio, S Pagliarani, F Russo… - arXiv preprint arXiv …, 2024 - arxiv.org
The paper is concerned with a McKean-Vlasov type SDE with drift in anisotropic Besov
spaces with negative regularity and with degenerate diffusion matrix under the weak H {\" o} …
spaces with negative regularity and with degenerate diffusion matrix under the weak H {\" o} …
Schauder type estimates for degenerate Kolmogorov equations with Dini continuous coefficients
We study the regularity properties of the second order linear operator in $\mathbb {R}^{N+ 1}
$:\begin {equation*}\mathscr {L} u:=\sum_ {j, k= 1}^{m} a_ {jk}\partial_ {x_j x_k}^ 2 u+\sum …
$:\begin {equation*}\mathscr {L} u:=\sum_ {j, k= 1}^{m} a_ {jk}\partial_ {x_j x_k}^ 2 u+\sum …
Optimal regularity for degenerate Kolmogorov equations with rough coefficients
G Lucertini, S Pagliarani, A Pascucci - arXiv preprint arXiv:2204.14158, 2022 - arxiv.org
We consider a class of degenerate equations satisfying a parabolic H\" ormander condition,
with coefficients that are measurable in time and H\" older continuous in the space variables …
with coefficients that are measurable in time and H\" older continuous in the space variables …
Intrinsic H\" older spaces for fractional kinetic operators
M Manfredini, S Pagliarani, S Polidoro - arXiv preprint arXiv:2309.16350, 2023 - arxiv.org
We introduce anisotropic H\" older spaces useful for the study of the regularity theory for non
local kinetic operators $\mathcal {L} $ whose prototypal example is\begin {equation}\mathcal …
local kinetic operators $\mathcal {L} $ whose prototypal example is\begin {equation}\mathcal …