Advances in Differential Equations

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

Yuxin Ge and Dong Ye

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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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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.

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