Stability of Solution of a Class of Quasilinear Elliptic Equations  

作　　者：Qi-kang Ran, Ai-nong FangDepartment of Applied Mathematics, Shanghai University of Finance and Economics, Shanghai 200433, ChinaDepartment of Applied Mathematics, Shanghai Jiaotong University, Shanghai 200030, China 

出　　处：《Acta Mathematicae Applicatae Sinica》2002年第3期461-470,共10页应用数学学报（英文版）

基　　金：the National Natural Science Foundation of China (No.19531060).

摘　　要： In this paper, using capacity theory and extension theorem of Lipschitz functions we first discuss the uniqueness of weak solution of nonhomogeneous quasilinear elliptic equationsin space W(θ,p)(Ω), which is bigger than W1,p(Ω). Next, using revise reverse Holder inequality we prove that if ωc is uniformly p-think, then there exists a neighborhood U of p, such that for all t ∈U, the weak solutions of equation corresponding t are bounded uniformly. Finally, we get the stability of weak solutions on exponent p.In this paper, using capacity theory and extension theorem of Lipschitz functions we first discuss the uniqueness of weak solution of nonhomogeneous quasilinear elliptic equationsin space W(θ,p)(Ω), which is bigger than W1,p(Ω). Next, using revise reverse Holder inequality we prove that if ωc is uniformly p-think, then there exists a neighborhood U of p, such that for all t ∈U, the weak solutions of equation corresponding t are bounded uniformly. Finally, we get the stability of weak solutions on exponent p.

关 键 词：Nonhoraogeneous quasilinear elliptic equations capacity STABILITY 

分 类 号：O175.25[理学—数学]