Liouville theorem for X-elliptic operators

We prove a Liouville-type theorem for a class of degenerate elliptic operators of the form Lu≔∑i,j=1N∂xi(aij∂xju)+∑i=1Nbi∂xiu.LL is supposed to be XX-elliptic, with respect to a family X=(X1,…,Xm)X=(X1,…,Xm) of locally Lipschitz continuous vector fields, in the sense introduced in [E. Lanconelli, A.E. Kogoj, XX-elliptic operators and XX-control distances, Contributions in Honor of the Memory of Ennio De Giorgi, Ricerche di Matematica 49 (Suppl.) (2000) 223–243].