AN ASYMPTOTIC EXPANSION OF THE SOLUTION OF A SECOND ORDER ELLIPTIC EQUATION WITH PERIODIC RAPIDLY OSCILLATING COEFFICIENTS
AN ASYMPTOTIC EXPANSION OF THE SOLUTION OF A SECOND ORDER ELLIPTIC EQUATION WITH PERIODIC RAPIDLY OSCILLATING COEFFICIENTS
复制标题
具有周期性快速振荡系数的二阶椭圆方程解的渐近展开式
DOI：
10.1070/sm1982v043n02abeh002444
复制
发表时间：
1982
期刊：
影响因子：
--
通讯作者：
E. V. Sevost'janova
中科院分区：
文献类型：
--
作者：
E. V. Sevost'janova
本文研究了在全空间上指定的方程基本解的渐近性态，如。系数是满足椭圆性、对称性和无穷光滑性条件的周期函数，主要结果是构造了形式为的渐近性，其中是任意正整数，在第一个参数中是齐次的，在其余参数中是周期的，对于集合上的余项，估计成立，其中常数与，无关，和.参考书目：九个头衔。
This paper studies the asymptotic behavior of the fundamental solution of the equation specified on the whole space , , as . The coefficients are periodic functions which satisfy the conditions of ellipticity, symmetry, and infinite smoothness.The main result is the construction of the asymptotics of in the form where is an arbitrary positive integer, the are homogeneous of degree in the first argument and periodic in the remaining arguments, and for the remainder term on the set , , the estimate holds, where the constants are independent of , , and .Bibliography: 9 titles.