Stratified Lie Groups and Potential Theory for Their Sub-Laplacians

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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Bonfiglioli, Andrea (Autor), Lanconelli, Ermanno (Autor), Uguzzoni, Francesco (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2007.
Edición:1st ed. 2007.
Colección:Springer Monographs in Mathematics,
Temas:
Algebra.
Differential equations.
Potential theory (Mathematics).
Topological groups.
Lie groups.
Differential Equations.
Potential Theory.
Topological Groups and Lie Groups.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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.

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