AI 中文总结
研究二维拟线性电导率的部分数据卡尔德隆问题，核心方法是基于高阶线性化及利用二维中部分边界消失的CGO解，通过改进余项估计、分析相位组合模式，最终证明唯一性结果。
AI 中文摘要
本文证明了二维拟线性电导率的部分数据卡尔德隆问题的唯一性结果。证明基于高阶线性化和二维中在部分边界上消失的复几何光学（CGO）解的使用。由于解的导数出现在积分恒等式中，我们需要改进的余项估计，为此我们在相位选择上引入一种修改，类似于极限卡尔曼权重。我们还分析了相位组合如何在解乘积中产生特定模式，这使我们能够应用驻相和非驻相论证来恢复电导率。
英文摘要
In this paper, we prove a uniqueness result for the partial data Calderón problem with quasilinear conductivity in two dimensions. The proof is based on higher-order linearization and the use of CGO solutions in dimension two that vanish on part of the boundary. Since derivatives of the solutions appear in the integral identity, we need improved remainder estimates, for which we introduce a modification in the choice of the phase, analogous to limiting Carleman weights. We also analyze how combinations of phases produce specific patterns in the products of solutions, which allows us to apply both stationary and nonstationary phase arguments to recover the conductivity.
