中文摘要：

对于一类主项系数为平方可积的椭圆型偏微分方程，我们证明其弱解的存在性．具体地说，考虑Ω中的方程- j（aij（x） iu）=f^0＋ if^i，u在边界取值为0，满足aij=aji,aij一致椭圆且aij∈L^2（ω）.在本文中，我们通过aij^（m）逼近aij，而aij^（m）属于L^∞（Ω），进而利用已知的关于椭圆型偏微分方程的可解性结果以及标准的能量方法来证明边值问题的存在性．

英文摘要：

In this paper we give the existence of weak solutions to a second order elliptic partial differential equation with square integrable regularity of leading coefficients. Specifically, we consider the elliptic equation - π （aij （x） iu） = f^0 - if^i in Ω,u = 0 on the boundary, with aij= aji, ,aij uniform elliptic, and aij ∈ L^2 （Ω）. First, we approximate aij by aij^（m） which belongs to L^∞ （Ω）, and then prove the existence theorem by applying the well known results concerning solvability of elliptic partial differential equation together with the standard energy method.