关于主项系数为平方可积的椭圆型偏微分方程解的一个存在性定理（英文）  

An Existence Theorem on Elliptic Partial Differential Equation with Square Integrable Leading Coefficients

作　　者：李扬[1] 

机构地区：[1]南京大学数学系,南京210093

出　　处：《数学理论与应用》2016年第3期37-41,共5页Mathematical Theory and Applications

基　　金：国家自然科学基金项目(11571167)资助

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(a_(ij)(x)_(iu))=f^0+_if^i,u在边界取值为0,满足a_(ij)=a_(ji),a_(ij)一致椭圆且a_(ij)∈L^2(Ω).在本文中,我们通过a_(ij)^((m)) 逼近a_(ij),而a_(ij)^((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.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.

关 键 词：椭圆型方程 存在性 能量方法 

分 类 号：O175.25[理学—数学]