论文标题
各向异性分数电导率方程的唯一性
Uniqueness for the anisotropic fractional conductivity equation
论文作者
论文摘要
在本文中，我们研究了分数各向异性电导率的反问题。我们的非局部运算符基于非局部载体计算的发达理论，并且与光谱获得的经典各向异性电导率算子的其他概括有很大差异。我们表明，各向异性电导率矩阵可以从分数dirichlet到neumann数据唯一恢复到天然量规。我们的分析利用了最近开发的技术来研究各向同性分数方程，并将其推广到不可分割的各向异性电导率的情况下。我们研究的动机源于它与古典各向异性Calderón问题的关系，在撰写本文时，该问题是该领域的主要开放问题之一。
In this paper we study an inverse problem for fractional anisotropic conductivity. Our nonlocal operator is based on the well-developed theory of nonlocal vector calculus, and differs substantially from other generalizations of the classical anisotropic conductivity operator obtained spectrally. We show that the anisotropic conductivity matrix can be recovered uniquely from fractional Dirichlet-to-Neumann data up to a natural gauge. Our analysis makes use of techniques recently developed for the study of the isotropic fractional elasticity equation, and generalizes them to the case of non-separable, anisotropic conductivities. The motivation for our study stems from its relation to the classical anisotropic Calderón problem, which at the time of writing is one of the main open problems in the field.
