359 citations · 778 across the 18 of their papers we have counts for
22 papers
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…
Struwe's Global Compactness and energy approximation of the critical Sobolev embedding in the Heisenberg group
Giampiero Palatucci, Mirco Piccinini, Letizia Temperini
We investigate some of the effects of the lack of compactness in the critical Folland-Stein-Sobolev embedding in very general (possible non-smooth) domains, by proving via De Giorg…
Global Compactness, subcritical approximation of the Sobolev quotient, and a related concentration result in the Heisenberg group
Giampiero Palatucci, Mirco Piccinini, Letizia Temperini
We investigate some effects of the lack of compactness in the critical Sobolev embedding in the Heisenberg group.
Nonlinear fractional equations in the Heisenberg group
Giampiero Palatucci, Mirco Piccinini
We deal with a wide class of nonlinear nonlocal equations led by integro-differential operators of order , with summability exponent and differentiability…
Asymptotic approach to singular solutions for the CR Yamabe equation
Giampiero Palatucci, Mirco Piccinini
We study the loss of compactness for optimal functions of a subcritical approximations of the sharp Folland-Stein-Sobolev embedding in the Heisenberg group. When blow-up is prevent…
Nonlocal Harnack inequalities in the Heisenberg group
Giampiero Palatucci, Mirco Piccinini
We deal with a wide class of nonlinear integro-differential problems in the Heisenberg-Weyl group , whose prototype is the Dirichlet problem for the -fractional su…