Stratified Lie Groups and Potential Theory for their Sub-Laplacians

• Main Authors: Bonfiglioli, A. (Author), Lanconelli, E. (Author), Uguzzoni, F. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2007.
• Series: Springer Monographs in Mathematics,
• Subjects: Mathematics.; Algebra.; Topological groups.; Lie groups.; Partial differential equations.; Potential theory (Mathematics).; Partial Differential Equations.; Potential Theory.; Topological Groups, Lie Groups.

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 exte...

Table of Contents:

• Elements of Analysis of Stratified Groups
• Stratified Groups and Sub-Laplacians
• Abstract Lie Groups and Carnot Groups
• Carnot Groups of Step Two
• Examples of Carnot Groups
• The Fundamental Solution for a Sub-Laplacian and Applications
• Elements of Potential Theory for Sub-Laplacians
• Abstract Harmonic Spaces
• The ?-harmonic Space
• ?-subharmonic Functions
• Representation Theorems
• Maximum Principle on Unbounded Domains
• ?-capacity, ?-polar Sets and Applications
• ?-thinness and ?-fine Topology
• d-Hausdorff Measure and ?-capacity
• Further Topics on Carnot Groups
• Some Remarks on Free Lie Algebras
• More on the Campbell–Hausdorff Formula
• Families of Diffeomorphic Sub-Laplacians
• Lifting of Carnot Groups
• Groups of Heisenberg Type
• The Carathéodory–Chow–Rashevsky Theorem
• Taylor Formula on Homogeneous Carnot Groups.