论文标题
关于Calderón的反向纳入问题，通过单个部分边界测量来平滑形状
On Calderón's inverse inclusion problem with smooth shapes by a single partial boundary measurement
论文作者
论文摘要
我们关注的是calderón的反夹杂物问题，其中一个人打算恢复相关边界测量嵌入均匀电导率中的不均匀导电夹杂物的形状。我们考虑了一个极具挑战性的案例，其单个部分边界测量构成了文献中长期存在的开放问题。在几项现有作品中显示，角奇异点可以帮助解决此反问题的唯一性和稳定性问题。在本文中，我们表明角落的奇异性可以放松，成为某种高壮观条件，并得出新颖的局部独特确定结果。据我们所知，这是通过单个（部分）边界测量来确定具有一般平滑形状的导电夹杂物的第一个（局部）唯一性。
We are concerned with the Calderón inverse inclusion problem, where one intends to recover the shape of an inhomogeneous conductive inclusion embedded in a homogeneous conductivity by the associated boundary measurements. We consider the highly challenging case with a single partial boundary measurement, which constitutes a long-standing open problem in the literature. It is shown in several existing works that corner singularities can help to resolve the uniqueness and stability issues for this inverse problem. In this paper, we show that the corner singularity can be relaxed to be a certain high-curvature condition and derive a novel local unique determination result. To our best knowledge, this is the first (local) uniqueness result in determining a conductive inclusions with general smooth shapes by a single (partial) boundary measurement.
