16 citations · 47 across the 18 of their papers we have counts for
21 papers
A study of the Kuramoto model for synchronization phenomena based on degenerate Kolmogorov-Fokker-Planck equations
Giulio Pecorella, Sergio Polidoro, Cecilia Vernia
We study a nonlinear partial differential equation that arises when introducing inertial effects in the Kuramoto model. Based on the known theory of degenerate Kolmogorov operators…
Mean value formulas for classical solutions to subelliptic evolution equations in stratified Lie groups
Diego Pallara, Sergio Polidoro
We prove mean value formulas for classical solutions to second order linear differential equations in the form w…
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…
Hölder continuity and boundedness estimates for nonlinear fractional equations in the Heisenberg group
Maria Manfredini, Giampiero Palatucci, Mirco Piccinini +1
We extend the celebrate De Giorgi-Nash-Moser theory to a wide class of nonlinear equations driven by nonlocal, possibly degenerate, integro-differential operators, whose model is t…
Mean value formulas for classical solutions to some degenerate elliptic equations in Carnot groups
Diego Pallara, Sergio Polidoro
We prove surface and volume mean value formulas for classical solutions to uniformly elliptic equations in divergence form with Hölder continuous coefficients. The kernels appearin…
Mean value formulas for classical solutions to uniformly parabolic equations in divergence form
Emanuele Malagoli, Diego Pallara, Sergio Polidoro
We prove surface and volume mean value formulas for classical solutions to uniformly parabolic equations in divergence form. We then use them to prove the parabolic strong maximum…
The Dirichlet problem for a family of totally degenerate differential operators
Maria Manfredini, Mirco Piccinini, Sergio Polidoro
In the framework of Potential Theory we prove existence or the Perron-Weiner-Brelot-Bauer solution to the Dirichlet problem related to a family of totally degenerate, in the sense…
A Yosida's parametrix approach to Varadhan's estimates for a degenerate diffusion under the weak Hörmander condition
Stefano Pagliarani, Sergio Polidoro
We adapt and extend Yosida's parametrix method, originally introduced for the construction of the fundamental solution to a parabolic operator on a Riemannian manifold, to derive V…
Schauder type estimates for degenerate Kolmogorov equations with Dini continuous coefficients
Sergio Polidoro, Annalaura Rebucci, Bianca Stroffolini
We study the regularity properties of the second order linear operator in : \begin{equation*} \mathscr{L} u := \sum_{j,k= 1}^{m} a_{jk}\partial_{x_j x_k}^2 u + \s…
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…
Fundamental solutions for Kolmogorov-Fokker-Planck operators with time-depending measurable coefficients
Marco Bramanti, Sergio Polidoro
We consider a Kolmogorov-Fokker-Planck operator of the kind studied by Lanconelli-Polidoro in [Rend. Sem. Mat. Univ. Politec. Torino 52 (1994)], where the leading coefficients $a_{…
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 compactness result for the Sobolev embedding via potential theory
Filippo Camellini, Michela Eleuteri, Sergio Polidoro
In this note we give a proof of the Sobolev and Morrey embedding theorems based on the representation of functions in terms of the fundamental solution of suitable partial differen…
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…
Gaussian lower bounds for non-homogeneous Kolmogorov equations with measurable coefficients
Alberto Lanconelli, Andrea Pascucci, Sergio Polidoro
We prove Gaussian upper and lower bounds for the fundamental solutions of a class of degenerate parabolic equations satisfying a weak Hormander condition. The bound is independent…
Harnack inequalities and Bounds for Densities of Stochastic Processes
Gennaro Cibelli, Sergio Polidoro
We consider possibly degenerate parabolic operators in the form that are naturally associated to a suitable family of stochastic d…
Sharp Estimates for Geman-Yor Processes and applications to Arithmetic Average Asian options
Gennaro Cibelli, Sergio Polidoro, Francesco Rossi
We prove the existence and pointwise lower and upper bounds for the fundamental solution of the degenerate second order partial differential equation related to Geman-Yor stochasti…
Harnack inequality for hypoelliptic second order partial differential operators
Alessia E. Kogoj, Sergio Polidoro
We consider nonnegative solutions of second order hypoelliptic equations \begin{equation*} \mathscr{L} u(x) =\sum_{i,j=1}^n \partial_{x_i} \left(a_{…
On Liouville-type theorems and the uniqueness of the positive Cauchy problem for a class of hypoelliptic operators
Alessia E. Kogoj, Y. Pinchover, S. Polidoro
This note contains a representation formula for positive solutions of linear degenerate second-order equations of the form $$ \partial_t u (x,t) = \sum_{j=1}^m X_j^2 u(x,t) + X_0 u…
Two-sided bounds for degenerate processes with densities supported in subsets of R^N
Chiara Cinti, Stephane Menozzi, Sergio Polidoro
We obtain two-sided bounds for the density of stochastic processes satisfying a weak Hörmander condition. In particular we consider the cases when the support of the density is not…