RECOVERING SINGULARITIES FROM BACKSCATTERING IN TWO DIMENSIONS
RECOVERING SINGULARITIES FROM BACKSCATTERING IN TWO DIMENSIONS
复制标题
从二维后向散射中恢复奇点
DOI：
10.1081/pde-100001768
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发表时间：
2001
影响因子：
1.9
通讯作者：
V. Serov
中科院分区：
文献类型：
--
作者：
P. Ola;L. Päivärinta;V. Serov
我们已经证明在二维中量子力学散射势的先导奇点是由后向散射数据决定的。我们假设短程势属于一个合适的加权Sobolev空间，并且通过估计born -展开中的迭代项，我们能够证明，例如对于平滑超表面上的heavisides型奇点，跳跃的位置和大小都可以从后向散射中恢复。证明的主要部分在于对第一个非线性Born-term进行足够精确的估计。这些估计被证明使用最近的表征w1，p -函数由于p . Hajlasz，和经典的triiebel的极大不等式的修改。
We have shown that in two dimensions the leading singularities of the quantum mechanical scattering potential are determined by the backscattering data. We assume that the short range potential belongs to a suitable weighted Sobolev space, and by estimating the iterative terms in the Born-expansion we are able to show, that for example for Heaviside-type singularities across a smooth hypersurface, both the location and the size of the jump are recovered from backscattering. The main part of the proof consists in getting sharp enough estimates for the first non-linear Born-term. These estimates are proven using a recent characterization of W 1,p -functions due to P. Hajlasz, and a modification of the classical Triebel's Maximal Inequality.