Partial data inverse problems for quasilinear conductivity equations
Partial data inverse problems for quasilinear conductivity equations
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DOI：
10.1007/s00208-022-02367-y
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发表时间：
2020-10
影响因子：
1.4
通讯作者：
Yavar Kian;Katya Krupchyk;G. Uhlmann
中科院分区：
文献类型：
--
作者：
Yavar Kian;Katya Krupchyk;G. Uhlmann
我们证明，对于一类半线性和拟线性电导率方程，在光滑区域边界的任意开放非空部分上给出的Dirichlet-to-Neumann映射的知识，唯一地决定了非线性电导率。证明的主要成分是一个涉及调和函数的梯度积和的一定密度结果，调和函数在边界的闭固有子集上消失。
We show that the knowledge of the Dirichlet-to-Neumann maps given on an arbitrary open non-empty portion of the boundary of a smooth domain in,, for classes of semilinear and quasilinear conductivity equations, determines the nonlinear conductivities uniquely. The main ingredient in the proof is a certain-density result involving sums of products of gradients of harmonic functions which vanish on a closed proper subset of the boundary.