Stratified Lie Groups and Potential Theory for their Sub-Laplacians

  • A. Bonfiglioli
  • E. Lanconelli
  • F. Uguzzoni

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages I-XXVI
  2. Elements of Analysis of Stratified Groups

  3. Elements of Potential Theory for Sub-Laplacians

  4. Further Topics on Carnot Groups

About this book

Introduction

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.

Keywords

Algebra algebra Potential theory Stratified Lie groups Subelliptic-Laplacians Vector field maximum principle partial differential equation

Authors and affiliations

  • A. Bonfiglioli
    • 1
  • E. Lanconelli
    • 1
  • F. Uguzzoni
    • 1
  1. 1.Dip.to MatematicaUniversità BolognaBolognaItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-71897-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 2007
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-71896-3
  • Online ISBN 978-3-540-71897-0
  • Series Print ISSN 1439-7382
  • About this book