Advances in Differential Equations

Some comparison, symmetry and monotonicity results for Carnot-Carathéodory spaces

Yuxin Ge and Dong Ye

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


We consider here some differential operators arising from the so called Carnot-Carathéodory metric spaces associated with a family of vector fields $X = (X_1, \ldots, X_k)$, which include the Hörmander type as a special case. We prove some weak and strong comparison results for solutions of the relevant differential $inequalities$. We then use these results to get some symmetry and monotonicity properties of solutions of the relevant partial differential equations.

Article information

Adv. Differential Equations Volume 6, Number 1 (2001), 51-72.

First available in Project Euclid: 2 January 2013

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Primary: 35R45: Partial differential inequalities
Secondary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc. 35B50: Maximum principles 35J70: Degenerate elliptic equations


Ge, Yuxin; Ye, Dong. Some comparison, symmetry and monotonicity results for Carnot-Carathéodory spaces. Adv. Differential Equations 6 (2001), no. 1, 51--72.

Export citation