The Glassey conjecture for nontrapping obstacles
The Glassey conjecture for nontrapping obstacles
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DOI：
10.1016/j.jde.2015.02.023
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发表时间：
2013-12
期刊：
影响因子：
--
通讯作者：
Chengbo Wang
中科院分区：
文献类型：
--
作者：
Chengbo Wang
我们验证了外域（M, g）的三维Glassey猜想，其中度规g是渐近欧几里德的，只要满足某些局部能量假设。对于三维或更高的维度，也验证了球外部的径向Glassey猜想。局部能量假设在许多重要情况下都得到满足，包括具有非捕获障碍和平坦度规的外域，具有星形障碍和小渐近欧几里德度规的外域，以及非捕获渐近欧几里德流形（R n, g）。
We verify the 3-dimensional Glassey conjecture for exterior domain (M, g), where the metric g is asymptotically Euclidean, provided that certain local energy assumption is satisfied. The radial Glassey conjecture exterior to a ball is also verified for dimension three or higher. The local energy assumption is satisfied for many important cases, including exterior domain with nontrapping obstacles and flat metric, exterior domain with star-shaped obstacle and small asymptotically Euclidean metric, as well as the nontrapping asymptotically Euclidean manifolds (R n, g).