# Stratified Lie groups and potential theory for their sub-Laplacians

@inproceedings{Bonfiglioli2007StratifiedLG,
title={Stratified Lie groups and potential theory for their sub-Laplacians},
author={Andrea Bonfiglioli and Ermanno Lanconelli and Francesco Uguzzoni},
year={2007}
}
• Published 2007
• Mathematics
The existence, for every sub-Laplacian, of a homogeneous fundamental solution smooth out of the origin, plays a crucial role in the book. This makes it possible to develop an exhaustive Potential Theory, almost completely parallel to that of the classical Laplace operator. This book provides an extensive treatment of Potential Theory for sub-Laplacians on stratified Lie groups. In recent years, sub-Laplacian operators have received considerable attention due to their special role in the theory…
600 Citations

### Wave equations on graded groups and hypoelliptic Gevrey spaces

The overall goal of this dissertation is to investigate certain classical results from harmonic analysis, replacing the Euclidean setting, the abelian structure and the elliptic Laplace operator with

### The obstacle problem for subelliptic non-divergence form operators on homogeneous groups

• Mathematics
• 2013
The main result established in this paper is the existence and uniqueness of strong solutions to the obstacle problem for a class of subelliptic operators in non-divergence form. The operators

### Local Invariants and Geometry of the sub-Laplacian on H-type Foliations

• Mathematics
• 2022
. H -type foliations ( M , H , g H ) are studied in the framework of subRiemannian geometry with bracket generating distribution deﬁned as the bundle transversal to the ﬁbers. Equipping M with the

### Regularity properties of spheres in homogeneous groups

• Mathematics
• 2015
We study left-invariant distances on Lie groups for which there exists a one-parameter family of homothetic automorphisms. The main examples are Carnot groups, in particular the Heisenberg group with

### Compact Embeddings, Eigenvalue Problems, and subelliptic Brezis-Nirenberg equations involving singularity on stratified Lie groups

• Mathematics
• 2022
. The purpose of this paper is threefold: ﬁrst we prove Sobolev-Rellich-Kondrachov type embeddings for the fractional Folland-Stein-Sobolev spaces on stratiﬁed Lie groups. Secondly, we study an

### Cohomology of annuli, duality and $L^\infty$-differential forms on Heisenberg groups

• Mathematics
• 2021
In the last few years the authors proved Poincaré and Sobolev type inequalities in Heisenberg groups H for differential forms in the Rumin’s complex. The need to substitute the usual de Rham complex

### A Cornucopia of Carnot groups in Low Dimensions

• Mathematics
• 2020
Stratified groups are those simply connected Lie groups whose Lie algebras admit a derivation for which the eigenspace with eigenvalue 1 is Lie generating. When a stratified group is equipped with a

## References

SHOWING 1-10 OF 13 REFERENCES