论文标题
线性本地操作员的高阶分数Calderón问题：独特性
The higher order fractional Calderón problem for linear local operators: uniqueness
论文作者
论文摘要
我们研究了分数Schrödinger方程（FSE）的反问题，该局部局部扰动是由小于分数laplacian的顺序的线性部分差分操作员（PDO）。我们表明，可以从与扰动的FSE相关的Dirichlet到Neumann（DN）图中唯一恢复PDO的系数。这对两类系数证明了这一点：属于Sobolev乘数和系数的某些空间的系数，这些系数属于属于有界导数的分数Sobolev空间。我们的研究概括了零和一阶扰动的最新结果对高阶扰动。
We study an inverse problem for the fractional Schrödinger equation (FSE) with a local perturbation by a linear partial differential operator (PDO) of order smaller than the order of the fractional Laplacian. We show that one can uniquely recover the coefficients of the PDO from the Dirichlet-to-Neumann (DN) map associated to the perturbed FSE. This is proved for two classes of coefficients: coefficients which belong to certain spaces of Sobolev multipliers and coefficients which belong to fractional Sobolev spaces with bounded derivatives. Our study generalizes recent results for the zeroth and first order perturbations to higher order perturbations.
