Notice bibliographique
- Notice
Type(s) de contenu et mode(s) de consultation : Texte noté : électronique
Auteur(s) : Bonfiglioli, Andrea
Titre(s) : Stratified Lie groups and potential theory for their sub-Laplacians [Texte électronique] / A. Bonfiglioli, E. Lanconelli, F. Uguzzoni
Publication : Berlin ; New York : Springer, cop. 2007
Description matérielle : 1 online resource (xxvi, 800 pages)
Collection : Springer monographs in mathematics
Note(s) : Includes bibliographical references (pages 773-787)-and indexes. - Print version record.
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 of linear
second-order PDE's with semidefinite characteristic form. It also provides a largely
self-c
Autre(s) auteur(s) : Lanconelli, Ermanno. Fonction indéterminée
Uguzzoni, Francesco. Fonction indéterminée
Sujet(s) : Analyse harmonique (mathématiques)
Espaces harmoniques
Groupes de Lie
Équations aux dérivées partielles
Potentiel, Théorie du
Groupes de Carnot
Indice(s) Dewey :
515.96 (23e éd.) = Théorie du potentiel ; 515.353 (23e éd.) = Équations différentielles partielles
Identifiants, prix et caractéristiques : ISBN 9783540718970
Identifiant de la notice : ark:/12148/cb446950600
Notice n° :
FRBNF44695060
(notice reprise d'un réservoir extérieur)
Table des matières : Part I: 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 ;
Part II: Elements of Potential Theory for sub-Laplacians; Abstract Harmonic Spaces
; The L-harmonic Space ; L-subharmonic Functions ; Representation Theorems ; Maximum
Principle on Unbounded Domains ; L-capacity, L-polar Sets and Applications ; L-thinness
and L-fine Topology ; d-Hausdorff Measure and L-capacity ; Part III: 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 Carnot Groups.
