Stratified Lie Groups and Potential Theory for their Sub-Laplacians [electronic resource] / by A. Bonfiglioli, E. Lanconelli, F. Uguzzoni.

By:

Bonfiglioli, A [author.]

Contributor(s):

Material type: Text

TextSeries: Springer Monographs in MathematicsPublisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2007Description: XXVI, 802 p. online resourceContent type:

text

Media type:

computer

Carrier type:

online resource

ISBN:

9783540718970

Subject(s):

Additional physical formats: Printed edition:: No titleDDC classification:

512 23

LOC classification:

QA150-272

Online resources:

Click here to access online

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.

In: Springer eBooksSummary: 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-contained presentation of stratified Lie groups, and of their Lie algebra of left-invariant vector fields. The presentation is accessible to graduate students and requires no specialized knowledge in algebra nor in differential geometry. It is thus addressed, besides PhD students, to junior and senior researchers in different areas such as: partial differential equations; geometric control theory; geometric measure theory and minimal surfaces in stratified Lie groups.

Holdings ( 1 )
Title notes ( 2 )

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Item type	Current library	Collection	Call number	Status	Date due	Barcode	Item holds
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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-contained presentation of stratified Lie groups, and of their Lie algebra of left-invariant vector fields. The presentation is accessible to graduate students and requires no specialized knowledge in algebra nor in differential geometry. It is thus addressed, besides PhD students, to junior and senior researchers in different areas such as: partial differential equations; geometric control theory; geometric measure theory and minimal surfaces in stratified Lie groups.