Oscillatory integrals and unique continuation for second order elliptic differential equations
Oscillatory integrals and unique continuation for second order elliptic differential equations
复制标题
二阶椭圆微分方程的振荡积分和唯一延拓
DOI：
--
复制
发表时间：
1989
期刊：
影响因子：
--
通讯作者：
C. Sogge
中科院分区：
文献类型：
--
作者：
C. Sogge
一个著名的反例（见[11]）表明，条件V E LPn 2是最好的可能性质。然而，这个反例必须从一个点而不是像定理1.1那样从开集进行唯一的连续。我们希望在以后的文章中从一个点开始讨论唯一连续。索耶[14]在低维情况下得到了常系数算子的这类结果，Jerison和Kenig [11]在一般n维情况下得到了这类结果。有很多以前的工作，我们建议读者[11，14]进一步参考。Jerison和Kenig证明了常系数算子从一点有唯一延拓的更强结果。对于变系数算子，我们的结果改进了H6rmander [8]中关于（1.1）的解存在唯一的开集延拓的结论
A well-known counterexample (see [11]) indicates that the condition V E LPn2 is in the best possible nature. This counterexample, however, has to do loc with unique continuation from a point rather than from open sets as in Theorem 1.1. We hope to treat unique continuation from a point in a subsequent paper. Results of this type for constant coefficient operators were obtained by Sawyer [14] for low dimensions and Jerison and Kenig [11] for general n. There was a lot of previous work, and we refer the reader to [11, 14] for further references. Also, Jerison and Kenig proved the stronger result that there is unique continuation from a point for constant coefficient operators. For variable coefficient operators our results improve one of H6rmander [8] which says that there is unique continuation from open sets for solutions to (1.1)