An inverse problem of Calderon type with partial data

On nonuniqueness for Calderon's inverse problem

We construct anisotropic conductivities with the same Dirichlet-to-Neumann map as a homogeneous isotropic conductivity. These conductivities are singular close to a surface inside the body.

关于渐近双曲流形反散射问题与Conformal Laplacian Calderón问题的相互作用

On the interplay between inverse scattering for asymptotically hyperbolic manifolds and the Calderón problem for the Conformal Laplacian

本文通过渐近双曲流形与Conformal Laplacian的关系，证明了特定能量下的散射矩阵能确定边界度量的jet结构。

A "milder" version of Calderón's inverse problem for anisotropic conductivities and partial data

Given a general symmetric elliptic operator $$ L\_{a} := \sum\_{k,,j=1}^d \p\_k (a\_{kj} \p\_j) + \sum\_{k=1}^d a\_k \p\_k - \p\_k(\overline{a\_k} .) + a\_0$$we define the associated Dirichlet-to-Neumann (D-t-N) operator with partial data, i.e., data supported in a part of the boundary. We prove positivity, $L^p$-estimates and domination properties for the semigroup associated with this D-t-N operator. Given $L\_a $ and $L\_b$ of the previous type with bounded measurable coefficients $a = \{a\_{kj}, \ a\_k, a\_0 \}$ and $b = \{b\_{kj}, \ b\_k, b\_0 \}$, we prove that if their partial D-t-N ope…

分数阶薛定谔算子在闭合黎曼流形上的加德纳问题

Calderón problem for fractional Schrödinger operators on closed Riemannian manifolds

研究分数阶薛定谔算子(-Δ_g)^α+V的类各向异性加德纳问题，证明通过解的柯西数据集可确定流形及势函数，结合新的反谱问题和非局部方程纠缠原理。

径向薛定谔算子的逆 Steklov 与 Calderón 问题中的局部 Hölder 稳定性及量化共振

Local Hölder Stability in the Inverse Steklov and Calderón Problems for Radial Schrödinger operators and Quantified Resonances

本文针对单位球上特殊 $L^2$ 径向势的薛定谔算子，利用 Steklov 频谱差的 Laplace 变换公式与矩稳定性估计，获得了逆 Steklov 与 Calderón 问题的局部 Hölder 稳定性，改进了先前的对数稳定性结果。

固定能量Calderón问题的Born近似

The Born approximation for the fixed energy Calderón problem

本文研究了固定能量下Calderón问题的Born近似，证明其作为径向分布的良定义性，并展示了其在恢复势中的应用及高能极限下的收敛性。