Pseudodifferential operators on Rn with bounded symbols
Pseudodifferential operators on Rn with bounded symbols
复制标题
Rn 上带有有界符号的伪微分算子
DOI：
10.1007/bf01075240
复制
发表时间：
1970
影响因子：
0.4
通讯作者：
V. Grushin
中科院分区：
文献类型：
--
作者：
V. Grushin
近年来伪微分算子理论的深入发展主要是研究紧致流形上的这些算子或研究它们的局部性质。在Rn上研究这类算子时，通常假定符号pix，~）在某种意义下稳定为x~ o。这里只要提到Kohn和Nirenberg [1]、塞利[2]、Volevich和Kagan [3]以及Hsrmander [4，5]的工作就够了。然而，有一些国家，在不满足x-~ oo的符号稳定性条件的情况下，得到Rn上的微分算子或伪微分算子的大量问题，这在MI Vishik和作者[6-9]的文章中已得到证明R1上的微分算子的研究对于发展退化于R1上的椭圆方程的边值问题的一般理论是必要的。一个区域的边界，椭圆伪微分算子理论的紧致流形上退化的子流形的余维1，和理论的边界值问题的椭圆方程，如果条件的椭圆是违反了子流形的边界余维1。
The very intensive development of the theory of pseudodifferential operators in recent years has been directed principally toward studying these operators on compact manifolds or studying their local properties. In studying such operators on R n it has usually been assumed that the symbol pix,~) is in some sense stabilized as x~~ o. It suffices here to refer to the work of Kohn and Nirenberg [1], Seeley [2], Volevich and Kagan [3], and HSrmander [4, 5]. There are, however, a great number of problems which lead to differential or pseudodifferential operators on R n without the condition of stabilization of the symbol for x--~ oo.It has been shown in the papers of MI Vishik and the author [6-9] that an investigation of differential operators on R 1 is necessary for the development of a general theory of boundary value problems for elliptic equations which degenerate on the boundary of a region, for the theory of elliptic pseudodifferential operators on a Compact manifold which degenerate on a submanifold of codimension 1, and for the theory of boundary value problems for elliptic equations if the condition of ellipticity is violated on a submanifold of the boundary of codimension 1.