Frequency of Harmonic functions in Carnot groups and for operators of Baouendi type
Analysis of PDEs
2012-12-27 v1
Abstract
We introduce a new notion of Almgren's frequency which is adapted to solutions of a sub-Laplacian (harmonic functions) on a Carnot group of arbitrary step . With this notion we investigate some new functionals associated with the frequency, and obtain monotonicity formulas for the relevant harmonic functions, or for the solutions of a closely connected class of degenerate second order operators of Baouendi type. The results proved in this paper provide some new insight into the deep link existing between the growth properties of the frequency, and the local and global structure of the relevant harmonic functions in these non-elliptic, or subelliptic, settings
Keywords
Cite
@article{arxiv.1212.6061,
title = {Frequency of Harmonic functions in Carnot groups and for operators of Baouendi type},
author = {Nicola Garofalo and Kevin Rotz},
journal= {arXiv preprint arXiv:1212.6061},
year = {2012}
}