Title: Direct reconstruction of anisotropic self-adjoint inclusions in the Calderón problem Show Chinese title

Title: 各向异性自伴包含物的直接重构在Calderón问题中

Abstract: We extend the monotonicity method for direct exact reconstruction of inclusions in the partial data Calder\'on problem, to the case of anisotropic conductivities in any spatial dimension $d\geq 2$. Specifically, from a local Neumann-to-Dirichlet map, we give reconstruction methods of inclusions based on unknown anisotropic self-adjoint perturbations to a known anisotropic conductivity coefficient. A main assumption is a definiteness condition for the perturbations near the outer inclusion boundaries. This additionally provides new insights into the non-uniqueness issues of the anisotropic Calder\'on problem. Show Chinese abstract

Abstract: 我们扩展了单调性方法，用于部分数据Calderón问题中夹杂物的直接精确重构，适用于任何空间维度的各向异性电导率$d\geq 2$。 具体而言，从局部Neumann-to-Dirichlet映射出发，我们给出了基于已知各向异性电导率系数的未知各向异性自伴扰动的夹杂物重构方法。 主要假设是在外夹杂物边界附近的扰动具有确定性条件。 这进一步为各向异性Calderón问题的非唯一性问题提供了新的见解。