The Carnot-Caratheodory Distance and the Infinite Laplacian

被引：10

作者：

Bieske, Thomas ^{[3
]}

Dragoni, Federica ^{[2
]}

Manfredi, Juan ^{[1
]}

机构：

[1] Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA

[2] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2AZ, England

[3] Univ S Florida, Dept Math, Tampa, FL 33620 USA

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2009年 / 19卷 / 04期

关键词：

Carnot-Caratheodory spaces; Infinite Laplacian; Viscosity solutions; LIPSCHITZ EXTENSIONS; HARMONIC-FUNCTIONS;

D O I：

10.1007/s12220-009-9087-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In a"e (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-Carath,odory 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.

引用

页码：737 / 754

页数：18

共 17 条

[1]

[Anonymous], 1996, Progress in Mathematics

[2]

Beatrous FH, 2005, CONTEMP MATH, V370, P1

[3] Lipschitz extensions on generalized Grushin spaces [J].