We consider the inverse problem of recovering an isotropic quasilinear conductivity from the Dirichlet-to-Neumann map when the conductivity depends on the solution and its gradient. We show that the conductivity can be recovered on an open subset of small gradients, hence extending a partial result to all real analytic conductivities. We also recover non-analytic conductivities with additional growth assumptions along large gradients. Moreover, the results hold for non-homogeneous conductivities if the non-homogeneous part is assumed known.

中文翻译：

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从边界测量中恢复准线性电导率

当电导率取决于解及其梯度时，我们考虑从 Dirichlet-to-Neumann 映射恢复各向同性拟线性电导率的逆问题。我们表明可以在小梯度的开放子集上恢复电导率，因此将部分结果扩展到所有实际分析电导率。我们还通过沿大梯度的额外增长假设来恢复非解析电导率。此外，如果假设非均质部分已知，则结果适用于非均质电导率。