Document Type

Contribution to Book

Publication Date

3-6-2008

Publication Title

Perspectives in Partial Differential Equations, Harmonic Analysis and Applications

Abstract

In this paper, we consider the Sub-Laplacian L which consists of sum of squares of smooth vector fields that satisfy Hormander's finite rank condition. We study the Dirichlet problem for this operator on domains that satisfy certain geometric conditions. For such domains, several key results are established. These results consist of 1) A reversed Holder inequality for the Poisson kernel 2) Harmonic measure (corresponding to L) and surface measure (as well as the H-Perimeter measure) are mutually absolutely continuous 3) A representation (hence solvability of the Dirichlet problem) for solutions to the Dirichlet problem.

Volume

79

First Page Number

49

Last Page Number

100

Version

Preprint

Publisher Statement

First published in Perspectives in Partial Differential Equations, Harmonic Analysis and Applications in Vol. 79, 2008, published by the American Mathematical Society.

Rights

Copyright 2008 by the American Mathematical Society

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