严子谦.一类拟线性椭圆方程组的Dirichlet问题[J].数学研究及应用,1985,5(4):127~128
一类拟线性椭圆方程组的Dirichlet问题
The Dirichlet Problem for a Class of Quasilinear Elliptic Systems
投稿时间:1983-11-30  
DOI:10.3770/j.issn:1000-341X.1985.04.034
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严子谦 吉林大学 
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英文摘要:
      The homogeneous Dirichlet problem(1) for quasilinear elliptic system in a bounded domain Ω is investigated in this paper. The existence of generalized solutions in [H01(Ω)]N is obtained by using the contructive Galerkin method. For the case of aijlm=0 when i≠j, it is estatablished that such generalized solutions have bounded [L(Ω)]N norm and possess Holeler continuity. Even in the particular case that fi are independent of Du, our results have improved those of A. V. Lair [Ann. Mat. Pura Appl., 116(1978)], allowing bi1(x,u) and fi(x,u) to have a growth in u arbitrarily close to 1.
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