摘要
具非负特征形式二阶微分方程的第一边值问题众所周知是Fichera提出的在边界子集∑_2∪∑_3上给值的形式.在主部系数矩阵最小特征值λ的负一次方为可积的条件下,辜联崑教授提出了只在∑_3上给值的另一形式.本文指出λ^(-1)的可积性会影响边界的划分,这种情况下整个边界除了一个零测集外全部是∑_3,因此第二种形式只是Fichera形式的特例.
The first boundary-value problem for second order equations with nonnegative characteristic form is known as the form giving value on the boundary-subset ∑_1∪∑_3, by FICHERA. Under the minimum eigenvalue of the principal coefficients matrix, to the minus one be integrable, prof. Gu Liankun proposed another form giving value only on ∑_3.This paper discuss the influence of λ^(-1)-integrability on the boundarydivision. In this case the boundary is all ∑_3 except a set of measure zero. Hence the second form is not a new but special case of FICHERA's.
出处
《应用数学》
CSCD
北大核心
1991年第2期97-100,共4页
Mathematica Applicata
关键词
微分方程
非负特征形式
点集Σ°
Differential equations of second order with no-negative characteristic form
Strict lipschitz domain
Point set
