Dirichlet Problems for the Quasilinear Second Order Subelliptic Equations

<正> In this paper, we study the Dirichlet problems for the following quasilinear secondorder sub-elliptic equation, sum from i,j=1 to m(Xi*(Ai,j（x,u）Xj u)+sum from j=1 to m(Bj（x,u）Xj u+C（x,u）=0 in Ω, u=φ on Ω,where X={X1, …, Xm} is a system of real smooth vector fields which satisfies the Hrmander’scondition, A（i,j）, Bj, C∈C∞（■×R） and (Ai,j（x, z）) is a positive definite matris. We have provedthe existence and the maximal regularity of solutions in the "non-isotropic" Hlder space associatedwith the system of vector fields X.