Frequency of Harmonic functions in Carnot groups and for operators of Baouendi type

2012/12/25 by Nicola Garofalo, Garofalo, Nicola, Kevin Rotz +1
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.1212.6061

openalex publication_date 2012/12/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \bG. 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

Citations

• Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian

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