谭启建,冷忠建.具间断系数的N维拟线性椭圆方程弱解的正则性[J].数学研究及应用,2008,28(4):779~788
具间断系数的N维拟线性椭圆方程弱解的正则性
The Regularity of the Weak Solutions for the $N$-Dimensional Quasilinear Elliptic Equations with Discontinuous Coefficients
投稿时间:2006-09-20  修订日期:2007-05-24
DOI:10.3770/j.issn:1000-341X.2008.04.005
中文关键词:  拟线性椭圆方程, 间断系数, 弱解, 正则性.
英文关键词:Quasilinear elliptic equation  discontinuous coefficients  weak solution  regularity.
基金项目:四川省教育学院科研基金(No.2006015).
作者单位
谭启建 四川教育学院数学系, 四川 成都 610041 
冷忠建 四川大学数学学院, 四川 成都 610064 
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中文摘要:
      讨论了具间断系数的N维拟线性椭圆方程. 利用估计和差分逼近方法,证明了弱解的一阶导数H\"{o}lder连续到方程系数间断的内边界.
英文摘要:
      The $n$-dimensional quasilinear elliptic equations with discontinuous coefficients are studied. Using estimate and difference approach methods, we prove that the first derivatives of the weak solutions are continuous in the sense of H\"{o}lder up to the inner boundary on which the coefficients are discontinuous.
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