论文标题
重建边界测量的粗糙电导率
Reconstruction of Rough Conductivities from Boundary Measurements
论文作者
论文摘要
我们展示了纳克曼程序的有效性（Ann。Math。，128（3）：531---576，1988）对于从其差异到Neumann Map $λ_γ$中重建电导率$γ$的有效性，以较小的常规电导率，特别是$γ\ in W^{3/2,2n}（3/2,2n}（$ 2）$ $ $ uce $。当加上$ 0 <s <1/2 $的$ 0 <s <1 <1/2 $时，我们还获得了反问题的对数型稳定性估计。
We show the validity of Nachman's procedure (Ann. Math., 128(3):531--576, 1988) for reconstructing a conductivity $γ$ from its Dirichlet-to-Neumann map $Λ_γ$ for less regular conductivities, specifically $γ\in W^{3/2,2n}(Ω)$ such that $γ\equiv 1$ near $\partial Ω$. We also obtain a log-type stability estimate for the inverse problem when in addition, $γ\in W^{2-s,n/s}(Ω)$ for $0 < s <1/2$.
