Dirichlet Problems for the Quasilinear Second Order Subelliptic Equations

作     者：Xu Chaojiang Department of Mathematics Wuhan University Wuhan, 430072 China 

作者机构：武汉大学数学系 湖北 武汉 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：1996年第12卷第1期

页      面：18-32页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Sub-elliptic equation Dirichlet problem A priori estimate 

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 Hrmander’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 Hlder space associatedwith the system of vector fields X.