当前位置: X-MOL 学术Rev. Mat. Iberoam. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
The double dispersion operator in backscattering: Hölder estimates and optimal Sobolev estimates for radial potentials
Revista Matemática Iberoamericana ( IF 1.2 ) Pub Date : 2020-12-08 , DOI: 10.4171/rmi/1223
Cristóbal Meroño 1
Affiliation  

We study the problem of recovering the singularities of a potential $q$ from backscattering data. In particular, we prove two new different estimates for the double dispersion operator $Q_2$ of backscattering, the first nonlinear term in the Born series. In the first, by measuring the regularity in the Hölder scale, we show that there is a one derivative gain in the integrablity sense for suitably decaying potentials $q\in W^{\beta,2}(\mathbb{R}^n)$ with $\beta \ge (n-2)/2$ and $n \ge 3$. In the second, we give optimal estimates in the Sobolev scale for $Q_2(q)$ when $n\ge 2$ and $q$ is radial. In dimensions 2 and 3 this result implies an optimal result of recovery of singularities from the Born approximation.

中文翻译:

背向散射中的双色散算子:Hölder估计和径向势的最佳Sobolev估计

我们研究了从反向散射数据中恢复潜在$ q $的奇异性的问题。特别是,我们证明了双色散算子$ Q_2 $的反向散射有两个新的不同估计,这是Born系列中的第一个非线性项。首先,通过测量Hölder尺度的正则性,我们表明在W ^ {\ beta,2}(\ mathbb {R} ^ n )$和$ \ beta \ ge(n-2)/ 2 $和$ n \ ge 3 $。在第二个中,当$ n \ ge 2 $和$ q $呈放射状时,我们以Sobolev规模给出$ Q_2(q)$的最佳估计。在维度2和3中,此结果表示从Born逼近恢复奇异点的最佳结果。
更新日期:2020-12-08
down
wechat
bug