Maximum principle and propagation for intrinsicly regular solutions of differential inequalities structured on vector fields ✩

We prove suitable versions of the weak maximum principle and of the maximum propagation for solutions u of a differential inequality Hu 0. Here H = i,j ai,j (z)ZiZj + Z0 is a differential operator structured on the vector fields Zj ’s, whereas u belongs to an appropriate intrinsic class of regularity modelled on the Zj ’s. © 2005 Elsevier Inc. All rights reserved