rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Stratified Lie Groups and Potential Theory for their Sub-Laplacians
  name:
    name part: Bonfiglioli, A.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Lanconelli, E.
    role:
      role term: author.
  name:
    name part: Uguzzoni, F.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2007
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XXVI, 802 p. online resource.
  abstract: 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.
  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.
  note: by A. Bonfiglioli, E. Lanconelli, F. Uguzzoni.
  subject:
    topic: Mathematics
  subject:
    topic: Algebra
  subject:
    topic: Topological groups
  subject:
    topic: Lie groups
  subject:
    topic: Partial differential equations
  subject:
    topic: Potential theory (Mathematics)
  subject:
    topic: Mathematics
  subject:
    topic: Algebra
  subject:
    topic: Partial Differential Equations
  subject:
    topic: Potential Theory
  subject:
    topic: Topological Groups, Lie Groups
  classification: QA150-272
  classification: 512
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Springer Monographs in Mathematics
  identifier: 9783540718970
  identifier: http://dx.doi.org/10.1007/978-3-540-71897-0
  record info:
    record creation date: 100301
    record change date: 20151204163257.0
    record identifier: 978-3-540-71897-0