Unique continuation from infinity for linear waves
Unique continuation from infinity for linear waves
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DOI：
10.1016/j.aim.2015.08.028
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发表时间：
2016-01-02
影响因子：
1.7
通讯作者：
Shao, Arick
中科院分区：
文献类型：
--
作者：
Alexakis, Spyros;Schlue, Volker;Shao, Arick
我们从类光无穷远处证明了各种唯一性结果，这些结果是针对渐近平直时空上的线性波的。假设在未来和过去类光无穷远的适当部分上解以无穷阶消失，我们推导出该解在内部的一个开集中必定为零。我们发现必须施加消失条件的无穷远部分强烈依赖于背景几何。特别地，对于具有正质量的背景（比如史瓦西或克尔背景），所需的假设比在闵可夫斯基时空中的假设要弱得多。这些结果在很多方面近乎最优。它们可被视为二阶椭圆算子的无穷远处唯一性结果的类似物。这项工作部分是由广义相对论中的问题所推动的。© 2015爱思唯尔公司。保留所有权利。
We prove various uniqueness results from null infinity, for linear waves on asymptotically flat space times. Assuming vanishing of the solution to infinite order on suitable parts of future and past null infinities, we derive that the.solution must vanish in an open set in the interior. We find that the parts of infinity where we must impose a vanishing condition depend strongly on the background geometry. In particular, for backgrounds with positive mass (such as Schwarzschild or Kerr), the required assumptions are much weaker than the ones in the Minkowski space time. The results are nearly optimal in many respects. They can be considered analogues of uniqueness from infinity results for second order elliptic operators. This work is partly motivated by questions in general relativity. (C) 2015 Elsevier Inc. All rights reserved.