Stability of the Inverse Conductivity Problem in the Plane for Less Regular Conductivities
Stability of the Inverse Conductivity Problem in the Plane for Less Regular Conductivities
复制标题
平面内较不规则电导率反电导率问题的稳定性
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
A. Ruiz
中科院分区：
文献类型：
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作者：
J. Barceló;Tomeu Barceló;A. Ruiz
Dirichlet到Neumann映射Λγ，或电压到电流的映射，将Dirichlet数据u=f∈∂Ω带到边界∂Ω处的余法导数γ和∂u∂η，其中u是椭圆型方程∂Ω(γ∇u)=0的解。在平面Lipitz域Ω⊂R2上，我们考虑了由γ在Ω内部的恢复组成的电导率逆问题，该问题由Λγ的知识组成。在假设各向同性电导率γ∈c1+e(Ω)的情况下，我们证明了这个逆映射的稳定性。我们将方程div(γ和∇u)=0化为等价系统，并使用∂∂散射变换。这种方法放宽了以往工作中对γ导数的要求。
Abstract The Dirichlet to Neumann map Λγ, or voltage to current map, takes Dirichlet data u=f∈∂Ω to the conormal derivatives γ ∂ u ∂ η at the boundary ∂Ω, where u is a solution to the elliptic equation div(γ ∇u)=0. On a plane Lipchitz domain Ω⊂R2, we consider the inverse conductivity problem that consists of the recovery of γ in the interior of Ω from the knowledge of Λγ. We prove stability for this inverse map, assuming an isotropic conductivity γ∈C1+e(Ω). We reduce the equation div(γ ∇u)=0 to an equivalent system and use the ∂∂-scattering transform. This approach relaxes the number of derivatives of γ required in former works.