The Carnot-Carathéodory Distance and the Infinite Laplacian

Bieske, T., Dragoni, Federica and Manfredi, J. J. 2009. The Carnot-Carathéodory Distance and the Infinite Laplacian. Journal of Geometric Analysis 19 (4) , pp. 737-754. 10.1007/s12220-009-9087-6

Full text not available from this repository.

Abstract

In ℝ n equipped with the Euclidean metric, the distance from the origin is smooth and infinite harmonic everywhere except the origin. Using geodesics, we find a geometric characterization for when the distance from the origin in an arbitrary Carnot-Carathéodory space is a viscosity infinite harmonic function at a point outside the origin. We show that at points in the Heisenberg group and Grushin plane where this condition fails, the distance from the origin is not a viscosity infinite harmonic subsolution. In addition, the distance function is not a viscosity infinite harmonic supersolution at the origin.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Carnot-Carathéodory spaces - Infinite Laplacian - Viscosity solutions
Publisher:	Springer
ISSN:	1050-6926
Last Modified:	04 Jun 2017 02:55
URI:	http://orca.cf.ac.uk/id/eprint/13889

Citation Data

Cited 8 times in Google Scholar. View in Google Scholar

Cited 7 times in Scopus. View in Scopus. Powered By Scopus® Data

Actions (repository staff only)

Edit Item