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