5 papers
Sub-Riemannian calculus and monotonicity of the perimeter for graphical strips
D. Danielli, N. Garofalo, D. M. Nhieu
We prove a monotonicity result at specific points for the Horizontal Perimeter for a class of surfaces in the Heisenberg group.
Interior Cauchy-Schauder estimates for the heat flow in Carnot-Caratheodory spaces
Donatella Danielli, Nicola Garofalo
The purpose of this paper is to establish some basic interior estimates of Cauchy-Schauder type for the heat flow associated with a system of smooth vector fields satisfying Horman…
Inequalities of Hardy-Sobolev type in Carnot-Carathéodory spaces
Donatella Danielli, Nicola Garofalo, Nguyen Cong Phuc
We consider various types of Hardy-Sobolev inequalities on a Carnot-Carathéodory space $(\Om, d)$ associated to a system of smooth vector fields on $\RR^n$…
Geometric second derivative estimates in Carnot groups and convexity
Nicola Garofalo
We prove some new a priori estimates for H_2-convex functions which are zero on the boundary of a bounded smooth domain Ωin a Carnot group G. Such estimates are global and are geom…
Mutual Absolute Continuity of Harmonic and Surface Measures for Hormander Type Operators
Luca Capogna, Nicola Garofalo, Duy-Minh Nhieu
In this paper, we consider the Sub-Laplacian L which consists of sum of squares of smooth vector fields that satisfy Hormander's finite rank condition. We study the Dirichlet probl…