3 papers
math.AP2026
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 a class of nonlocal hypoelliptic equations arising naturally in kinetic theory, in which a first-order transport operator is coupled wi…
math.AP2024
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…
math.AP2024
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…