Francesco Uguzzoni

A perturbation result for the Webster scalar curvature problem on the CR sphere

Abstract We consider the problem of prescribing the Webster scalar curvature on the unit sphere of C n+1 . Using a perturbation method, we obtain existence results for curvatures close to a positive constant and satisfying an assumption of Bahri–Coron type.

Nonlinear Liouville theorems for some critical problems on H-type groups

Abstract In this paper, we provide a non-existence result for a semilinear sub-elliptic Dirichlet problem with critical growth on the half-spaces of any group of Heisenberg-type. Our result improves a recent theorem in (Math. Ann. 315 (3) (2000) 453).

Non-divergence equations structured on Hörmander vector fields: heat kernels and Harnack inequalities

In this work the authors deal with linear second order partial differential operators of the following type

Fundamental solutions for non-divergence form operators on stratified groups

H=\partial_{t}-L=\partial_{t}-\sum_{i,j=1}^{q}a_{ij}(t,x) X_{i}X_{j}-\sum_{k=1}^{q}a_{k}(t,x)X_{k}-a_{0}(t,x)

Critical semilinear equations on the Heisenberg group: the effect of the topology of the domain

where

Harnack inequality for non-divergence form operators on stratified groups

X_{1},X_{2},\ldots,X_{q}

A LIOUVILLE-TYPE THEOREM ON HALFSPACES FOR THE KOHN LAPLACIAN

is a system of real Hormanders vector fields in some bounded domain

A note on lifting of Carnot groups

\Omega\subseteq\mathbb{R}^{n}

A multiplicity result for a degenerate elliptic equation with critical growth on noncontractible domains

,

Wiener-type tests from a two-sided Gaussian bound

A=\left\{ a_{ij}\left( t,x\right) \right\} _{i,j=1}^{q}