Overview

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.

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9786611066468

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Reviews

From the reviews: <p> The book is about sub-Laplacians on stratified Lie groups. The authors present the material using an elementary approach. They achieve the level of current research starting from the basic notions of differential geometry and Lie group theory. The book is full of extensive examples which illustrate the general problems and results. Exercises are included at the end of each chapter. a ] The book is clearly and carefully written. It will be useful for both the graduate student and researchers in different areas. (Roman Urban, Zentralblatt MATH, Vol. 1128 (6), 2008)

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