The Calderón problem for quasilinear elliptic equations
The Calderón problem for quasilinear elliptic equations
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拟线性椭圆方程的 Calderón 问题
DOI：
10.1016/j.anihpc.2020.03.004
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
G. Uhlmann
中科院分区：
文献类型：
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作者：
Claudio Muñoz;G. Uhlmann
本文证明了拟线性Calderon反问题电导率的唯一性。非线性电导率以非线性方式依赖于电势本身及其梯度。在正问题的某些结构假设下，允许复平面的小解析延拓的实值电导率诱导出唯一的Dirichlet-to-Neumann（DN）映射。证明的方法考虑了一些复值，线性测试功能的基础上的一个点的边界域，和线性化的DN映射放置在这些特定的一组解决方案。
In this paper we show uniqueness of the conductivity for the quasilinear Calderon's inverse problem. The nonlinear conductivity depends, in a nonlinear fashion, of the potential itself and its gradient. Under some structural assumptions on the direct problem, a real-valued conductivity allowing a small analytic continuation to the complex plane induce a unique Dirichlet-to-Neumann (DN) map. The method of proof considers some complex-valued, linear test functions based on a point of the boundary of the domain, and a linearization of the DN map placed at these particular set of solutions.