The Theorems of Bony and Brezis on Flow-Invariant Sets
The Theorems of Bony and Brezis on Flow-Invariant Sets
复制标题
流不变集上的 Bony 和 Brezis 定理
DOI：
10.1080/00029890.1972.11993115
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发表时间：
1972
影响因子：
0.5
通讯作者：
R. Redheffer
中科院分区：
文献类型：
--
作者：
R. Redheffer
其中[to，t1）是通过点x（to）的轨迹的存在区间。当解在to之外不存在时，条件被认为是空满足的。本文的目的是推广Bony [2]最近得到的关于流不变集的一个重要定理，并说明它与Brezis [3]的另一个定理的关系。这里的证明比迄今为止给出的证明简单，结果也更强。然而，本文是暂时性的。
where [to, t1) is the interval of existence for the trajectory through the point x(to). When the solution does not exist beyond to, the condition is considered to be vacuously fulfilled. Our objective is to generalize a remarkable theorem for flow-invariant sets that was recently obtained by Bony [2] and to show its relation to another theorem of Brezis [3]. The proofs here are simpler than those given hitherto, and the results are stronger. However, this paper is expository.