We establish a logarithmic stability estimate for the inverse problem of determining the nonlinear term, appearing in a semilinear boundary value problem, from the corresponding Dirichlet-to-Neumann map. Our result can be seen as a stability inequality for an earlier uniqueness result by Isakov and Sylvester (Commun Pure Appl Math 47:1403–1410, 1994).

中文翻译：

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半线性椭圆逆问题的稳定性估计

我们为确定非线性项的反问题建立了对数稳定性估计，该非线性项出现在半线性边值问题中，来自相应的Dirichlet-to-Neumann映射。我们的结果可以看作是Isakov和Sylvester先前的唯一性结果的稳定性不等式（Commun Pure Appl Math 47：1403–1410，1994）。