4 papers · 1 filter
The weak Harnack inequality and the rigidity of the anisotropic Trudinger's equation
Simone Ciani, Mattia Galeotti, Igor Skrypnik
We prove a local weak Harnack inequality for nonnegative weak super-solutions to the anisotropic Trudinger equation. As an application, we show a proof of the Harnack inequality th…
Critical concave-convex problems in Carnot groups
Mattia Galeotti, Eugenio Vecchi
We consider a model Dirichlet problem with concave-convex and critical nonlinearity settled in Carnot groups. Our aim is to prove the existence of two positve solutions in the spir…
Critical singular problems in Carnot groups
Stefano Biagi, Mattia Galeotti, Eugenio Vecchi
We consider a power-type mild singular perturbation of a Dirichlet semilinear critical problem settled in an open and bounded set in a Carnot group. Here, the term critical has to…
An extension to non-nilpotent groups of Rothschild-Stein lifting method
Mattia Galeotti
In their celebrated paper of 1976, Rothschild and Stein prove a lifting procedure that locally reduces to a free nilpotent Lie algebra any family of smooth vector fields $X_1,\dots…